It's a rating for the battery inside the device. It means that the battery can supply 3000 milli-Amps for one hour, or equivalent (e.g. 1500mA for two hours, or 6000mA for 30 minutes). This is at the voltage of the battery, typically 3.7V.
It's related to the amount of chemicals inside the battery that can be transformed from one type to another, releasing energy in the process.