Of course, Westeros is the main stage for A Song of Ice and Fire, but how important is it at a ... planetary scope?
There is a lot of civilisation beyond the Narrow Sea and, especially around the Narrow Sea, most of it is very evolved in terms of society and economy. Also the Dothraki may live a very wildling-ish life, but they appear neither afraid of nor foreign to higher cultures. There are also the Wildlings north of the wall, which also seems to be a large civilisation.
So how important is Westeros to the entire planet? Are they a few amongst many or are they the most sophisticated society on that planet and take a rather leading role?
More information I found
I rewatched the TV show and did a little army counting on the side. The numbers don't feel mathematically sound, but maybe the Westerosis are very good at accounting for losses in most recent battles, while I'm not. Give or take a few garrisons, all of Westeros has (had) about 300k soldiers. If I had to guess I'd say that's a little more than the Wildlings and all of Essos put together, but I can't find solid numbers on those. So, measuring in military size and assuming there aren't any other big inhabitated continents we don't know of, Westeros is about half the world. I'm still having trouble gauging the size of Essos.
In Yunkai alone, there are about 200k slaves (according to TV show S3E7). This allows for speculation that Yunkai alone has a population somewhere between 200k and 1m people. If Yunkai does not greatly outsize all other Free Cities, Essos probably has a much larger population than Westeros. Kings Landing has a population of 500k.