That's mA-Hr or milliAmp-Hour and is a measure of the batteries capacity at a rated discharge rate (see battery's data sheet or specs).
In general: a 1000mA-Hr battery discharged at a constant 200mA will last 5 hour. In particular the amount of time the battery will last with a constant discharge rate is dependent on the discharge rate compared to the discharge rating, the battery temperature and the internal condition of the battery's chemistry. But the simple relationship does suffice for must work.
