It's a multiplier to show how big current the battery can supply. Usually there are 2 of these: 30C / 15C or 50C / 25C, etc.
The first shows how big current it can supply for a short period of time (burst rate). Meaning seconds. The second is how much it can supply continuously. So on the trigger pull you get an impulse of high current that levels to the lower value in a few seconds.
The value itself is a multiplier to the capacity of the battery. So an 1000mAh battery with 20C rating gives 20x1000mA = 20A. An 1500mAh with 30C gives 45A.
Normal AEGs use about 15-20A.
If you have a battery that can't supply the needed current, the ROF will be lower, or the motor won't even be able to move the gears. (Because in this case the voltage drops, hence the beeping lipo guards on firing.)
High torque motors, powerful springs may need currents above 100 Amps. The more powerful your setup is, the more current it needs.