C rating affects the battery's ability to deliver current without heating. In essence its a measure of battery internal resistance.
Higher C means lower internal resistance and less heat (wasted energy) at the same power.
For our purposes there will be very little difference seen with 20C and higher rated batteries until you are going for some higher performance aircraft. Since 20C is the lowest C rating that is commonly available, you don't have to worry about C rating until you progress to high performance models and even then the 20C might be adequate.
I run 20C 5000 mah packs (3 X 4S for 12 or 50.4 V full charge) pulling 105 amp peak and 60 amp average with the plane in my Avatar pic and its just fine. Dropping in 30C packs I only see a marginal power increase... just 1 mph difference in top speed.