There are two completely different topics on where the terms "xC" are used when talking about lipo batteries. Of course "x" referring to a number.

1. Charging: When charging some batteries can only take a single digit multiple of their capacity. For example, most cheaper batteries can only be charged at 2C. Some of the higher end batteries can be charged at 5C. This is what determines how long does the battery have to stay on the charger.
2. Discharging: When discharging, batteries can provide a double digit multiple of their capacity. For example, most cheaper batteries can deliver 20C. With a burst of approx 30C. The higher end batteries can deliver much more than that, in the realm of approx 50C. This is how much you can extract from the battery at any particular SURGE without damaging the battery.

Hope this clears up the confusion a little.

Rafael