I only watched the Game of Thrones TV series. But there it was said that the current summer lasted for already nine years. In our world a "year" is the time in which all four seasons pass. Since this is different in Westeros, they seem to have some other way of saying what a "year" is. Is this somehow explained in the books?
It appears that a Year is measured the same way as it currently is for us, approximately 365 rotations of the planet or one trip around the sun. I have not found this stated explicitly though.
As for the changing of seasons I found the post below.
From "Westeros", A Wiki of Ice and Fire
Westeros is at the mercy of erratic seasons that may last for many years, but whose duration is unpredictable. At the beginning of A Song of Ice and Fire the continent has enjoyed a decade-long summer, and many fear that an equally long and harsh winter will follow. It is unclear to which degree the eastern continent is subject to the same conditions. George R. R. Martin explicitly and more than once stated that the explanation of the Planet's climate will be revealed at the end of the series, so he cannot disclose any further details on the issue before that point. He also stated that the explanation will be magical in nature and will not involve any sci-fi elements.
Martin has stated that they measure years according to the solar cycle:
[What is the cycle of a year? Why do they count years when seasons are strange?]
Twelve moon tuns to a year, as on earth. Even on our earth, years have nothing to do with the seasons, or with the cycles of the moon. A year is a measure of a solar cycle, of how long it takes the earth to make one complete revolution around the sun. The same is true for the world of Westeros. Seasons do not come into it.
To our mostly temperate climate perspective tracking seasons seems like the only significant reason to have a year, but even tropical cultures (such as the Maya) had devised solar calendars. The long term cycle of the stars seems to make a convenient unit of time.
So far it has not been explained in the books. I have not seen any evidence that the characters know anything about the rotation of their planet around its axis or around the sun. The do have "name days", though, which means they do have a notion of a year. There is also a moon, and a notion of a month, which means that the moon has phases. A reasonable explanation would be that a year is defined in terms of the months, but I saw nothing in the books that directly supports that.
Could be their planet is tilted somewhat like ours, so the days get shorter in what we call "winter". But their planet may be a bit closer to their star, so the effect doesn't come with the ice and snow that comes with low temperatures.
A year seems to be about the same length as our year. "Flowering" happens at about twelve, a six-year-old baby is weird, and 102-year-old Maester Aemon is described as the oldest man in Westeros (as far as that guy knows, anyway).
The years are at regular intervals, too. Cat notes her three-year-old is half as old as her weird six-year-old nephew (and five times as fierce).
Also keep in mind that astronomy doesn't seem to be the mystery here it seems to have been in Europe circa 1000. At least not among the literate. The maesters in this world have many links in their chains, for many fields, including a bronze for astronomy (according, uncited, to Wiki of Ice and Fire). They likely realize they're orbiting a star, and can watch the others move. Even if the days don't get shorter due to wobble, they can probably measure a rotation by telescope and chart.
As some people have stated they could be using a lunar calendar, but there's also the possibility of a celestial calender.
Saying a year as one trip around the sun may be a new-ish concept due to a lack of a solar system model with the sun at the center is semi misleading because one can still visibly chart that progress WITHOUT seasons by looking at the night sky.
Most constellations/asterisms are only visible for a portion of the year (the exceptions circum-polar stars). Early civilizations were aware of this hence the western zodiac. The zodiac functions with a sign being determined what constellation would appear to be a part of if we could see the stars by daylight. That constellation is then visible at night at its peak half a year after the sun was part of the constellation. The zodiac along with all other constellations become visible in nice regular intervals with lengths varying in how North/South a constellation is.
If Westeros uses a celestial calendar, which given the Maester's chain has a Bronze link for Astronomy (meaning astronomy is likely more than an idle hobby) then the year could easily be determined by the appearance of a given constellation or star as marking the start of a year or month ect. The constellation or star would remain visible for some time before vanishing and eventually it would re-appear marking a return of that date.
I got the solid impression that each year has 4 seasons as normal....but there are sort of iceages caused by magic that make "summer" and "winter" years. There were regular years and seasons in the real Ice Age. I think winter works like that and that's roughly what I'd imagine conditions in winter are like, drop Ice Age onto a medieval European society that's been partially modified as far as it could be to deal with it.
Ex: Planting cycles are mentioned, with Maesters taking temperature readings to tell when to plant which would be unnecessary if summer literally was summer with no seasons. I read summer as basically the natural temperate climate without magical interference, think America's Midwest region for much of the South and Canada for the North (like Canada, while colder the north isn't always covered in snow they still manage to support population have farms etc, it was just "summer snow" when we saw Winterfell with the dead direwolf)
Winter is an Ice Age of comparatively short duration and purely magical causes afflicting random seeming spans of years and sometimes decades (this 9 year season was abnormally long I remember, and a "3 year winter" was mentioned I think, as was one lasting an entire generation). You'd still get seasons in winter as well, such as false springs and spirit summers.
So a year has 4 "pseudo seasons (our fall winter spring and summer) and the word season in the book is meant like warm/cold cycles independent of years ("WINTER" and "SUMMER". with shorter transition periods of "SPRING" and "FALL")
So a year in summer goes like this
- planting cycle (spring)
- growing cycle (summer)
- harvest cycle (summer fall)
- summer snows (basically our winter, no big deal for westros)
A year in winter goes like this
- Fall...Very cold
- Winter...Very very cold
- False spring (still very cold but improvement.... We haven't seen one, but it's mentioned as something the Maesters can recognize and warn people that winter is still on regardless. so 1 it's recognizable and 2 it's good enough people could mistake it for winter ending) - Spirit summer (can we plant a little? is there thaw? do animals emerge from hibernation?)
So you can still track years, but SEASONS are also a big deal (and different than seasons). So far we've seen only SUMMER and FALL, but the book has been 3 years so we've likely seen seasons pass relatively unremarked aside from the summer snows at the start of the book and the planting times mentioned offhand in context of the war and winter approaching. it was something about burned fields and there not being another planting cycle in time to beat FALL
The Maesters can track seasons to advise on planting easily enough and collect and debate data to measure SEASONS and advise how much grain to store each year to avoid death by Ice Age
I would very probably stick to the idea that the irregular seasons are a phenomena that postdate the civilization. Possibly, they had 4 seasons at the begining, and all that crazy-Westeros stuff, like white walkers, The Wall, children of the forest desapearing, started when the seasons went crazy, so they kept their old time measuring habits.
Obviously the Westerosi notion of a year is separate from the seasons, so therefore it must be very different to our pre-industrial year, the tracking of which had so much relevance for agriculture and keeping alive. Personally I think Martin failed to release what he'd done to the notion of a year by messing up the seasons until much later. There are a couple of ways to explain the Westerosi concept of a year. Firstly, there could be a rotating moon that takes a year to cycle. If the moon is important enough to create our months, it may be enough to create the Westerosi year. Or, the year could be a culturally significant time period, rather than a natural one. If I were Martin I would create a story based around a main character's name day, and say that there would be an original four hundred gods or four hundred saints used by the Andals, and the cycle of those god's names became culturally significant enough for a person's name day to mark their age.
The first time I heard about the nine year summer, I thought that they had a double cycle of small normal seasons forming a year and a bigger cycle of short following warm and cold times like short period ice ages. But I found no further indication for that.
Now I think that that it's either a mistake by the author or a problem of describing Westeros in an earthborn language. We don't know which language the people in Westeros speak and how they measure their time. It is possible that the word year is only used to make the reader understand.
There is no explanation in the five books so far. As many have noted, time seems to be equivalent; moon cycles making up a calendar, and similar length of year, relative to our own standards. "Moons" are not fantasy; many early civilizations relied on a lunar calendar, and the Jewish, Moslem, and Chinese calendars - all still used - are all lunar-based. If people "seem older", remember that in a farming-and-herding level of technology - which still persists in many portions of our world - children have to start working, and start being both knowledgeable and realistic about life, much earlier than our typical extended adolescence through college. Consider that in the Old Testament a boy of 13 or girl of 12 was considered ready for adulthood and marriage, and that many cultures recognize 15 or 16 as being a "marriageable" age.
I asked myself the same question and I thought of a possibility:
A second moon is mentioned in the book, a moon that disappeared. Maybe that moon's cycle was 12 times longer than the moon that stayed. So they keep counting the days of that cycle, because its easier to measure the length of a season with that cycle. So they actually have two different months and not a month and a year.
Sorry if a had mistakes in spelling, English isn't my first language.
Both in the show and the book the characters have said a winter has last multiple years. A year is definetly the time period which a planet delays to go around its sun; i.e. when the planet comes closer, its what we know as summer, and when it goes further away its what we know for winter. To be compliant with gravity law a planet cannot get to have some years far away to its sun without having a transformation cicle making eliptical movements, unless it be turned this way artificially, i.e. by a god which may have an interest to have controlled the human population, causing death and destruction with an agent (starvation, and then a human killer monster) and then balance it again with a counter-agent (Azhor Ahai)
There are two obvious explanations.
The first is that the only seasons are the erratic long ones and there is some other astronomical cycle used to represent a year. There could be some reasonably obvious annual cycle such as movements of constellations of conjunctions of planets. We do know that the Citadel does make detailed but largely unspecified observations which allows them to predict the onset of winter some time in advance or at least declare that it is officially autumn. Also on a world where the major seasons are so erratic there is clearly a strong incentive to come up with a good calendar.
Also they very clearly have days so it may be that a Westeros year is just some arbitrary number of days. There is no sensible reason why this should correspond to an earth year but this may just be artistic license to make the text more readable, after all there is equally no sensible reason why they should be speaking English, especially considering that GRRRM's style is typically to keep the nuts and bolts details of the world familiar and apart form place names etc he doesn't do a lot of outright making up of details of language and culture for the sake of it.
The second option is that Westeros has mild seasons similar to earth (perhaps like the southern Mediterranean) which are noticeable but have little impact compared to the 'big' winters.
Based on how mature all the characters seem for their ages, I'd guess a year is significantly longer than our 365 days year - but how long is a day in Westeros? Ah, let's just say they're 24 hours.
I don't really think Mr. Martin stopped to consider the concept of time, because this should really have been addressed early in the books. Him for example telling us Dany is 14, only gives a rather vague indication.
But let's take Dany and Robb into account, Dany is said to be 14 but seems more like she's 15-16. And Robb is said to be 16, but seems more like about 18-19. This would mean that a year is indeed longer in Westeros, and I'd estimate that the year is about 400 earth-days long, which means that:
365 x age + (age x 35) / 365
would give you the characters age according to our "earth-year". Then again this is 100 % based on sourceless speculation.