"C' rating is used to designate the safe discharge of batteries
When you use a li-ion battery there is an internal resistance that creates heat and begins to shorten the life of the battery. This happens with every battery and is normal. The smaller the battery the greater the heat build up at a given discharge rate. To put it another way they have a limited lifespan. When the discharge rate exceeds the battery designs limits it creates more heat and accelerates the process sometimes to the point where the battery catches on fire or even explodes. There is an electronic switch in the battery that is supposed to shut of the current before it becomes a dangerous situation. Sometimes these switches fail and we read about the guy whose battery caught on fire. Usually you will just shorten the lifespan on the battery.
For more about C rating and safety:
Charles-Augustin de Coulomb's C-Rate for Batteries