battery's C (capacity) rating is the maximum safe continuous discharge rate of a battery.
A batteries maximum acceptable discharge rate is calculated by multiplying its current rating by it's C rating.
A C rating of 1 means the battery can be discharged at the same rate as its capacity.
So a 1 Amp (1000mah) battery with a Crating of 1 can be continuously discharged at 1 Amp.
A more typical example: 11.1 volt 2000mAh (2 amp) battery rated at 10C = 2 Amps x 10C = 20 amps continuous discharge.
You use the C rating to determine if a given battery has sufficient current available to drive your motor(s) at maximum output.
Exceeding the C rating for a significant period will result in damage to the battery and can cause it to burn or even explode.
Batteries also often indicate a second (safe) short term maximum C rating (commonly 50% over the continuous C rating).