In the book it describes the Lesser and Greater Circumstances as things that will affect a spell at any given time and they must be adjusted or compensated for. However I still don't understand why they matter at all. In South Brakebills Quentin ( as well as the other students I assume) would sit and do each spell adjusting for each Circumstance until that had done the spell for every circumstance, but the spell worked everytime despite none of the circumstances actually being there. I assumed that a spell would not work if you didn't account for the circumstances. So why do the Circumstances matter?
It is a way to make the magic of that universe seem like it was more of a science than anything else.
The Circumstances are things that could effect a spell. And to adjust for the different Circumstances wherever you are in the world is just a way to make sure the spell will work the way you want it to.
Think of when you are cooking some pasta. If you are a sea level, your water will boil at 212 deg F. If you are over 2000ft above sea level, you need to adjust the cooking time as the boiling point reduces to 208 deg F. Breads and cakes usually require additional adjustments such as increased dry ingredients and higher oven temperature at elevations above approximately 3500 ft.
Same goes in the Brakebills universe, wherever you are on the planet, what time of day, what time of year, etc will all effect the spell trying to be cast.
The boiling point of water is a great example. Think about this, if they had a spell to create a fireball, do you think the effectiveness of said fireball would be affected by the temperature outside? Could creating a fireball in the desert in the middle of the day be less/more effective than creating it in the middle of the night in the middle of the frozen tundra. You're factoring in that you have an energy source [sun] and different levels of water in the air [humidity] and many other things. I think Magicians bending the universe to will things to happen will depend on the universe's materials around them