mAh means milliamp Hour and is a unit that measures (electrical charge) power over time. It is commonly used to measure the potential energy capacity of a battery. In general, the higher the mAh rating, the longer the expected battery life before requiring recharging.
This can be used to provide an idea of how long a device will last, given a constant (or average) power draw rate. For instance, a 3000 mAh battery could power a device drawing 100 mA (milliamp) for 30 hours. A device drawing 200 mA would last only 15 hours.