1 C is defined relative to 1 hour for full discharge and 3 C means a 3x faster discharge rate (full capacity can safely be discharged in 1/3 hour, or you can discharge 3 cells sequentially in an hour). Good lithium cells tend to be above 5C, can reach 10C for peak load or if cooled.

For a large enough battery it doesn't really matter, but for dense portable ones a lower C rating means you have to discharge from more cells simultaneously to maintain a given output. That makes it more complicated, and you have less headroom to the battery's maximum Watt output if you need to accelerate a car hard suddenly.