The *mAh rating on a battery is an indicator of the maximum amount of current that the battery can deliver per hour and is generally an indicator of the capacity of the battery. However, this also depends largely on the voltage of the battery. The Watts (Wh) rating is a better indicator of capacity as this factors in the voltage as well.
Some batteries are rated in Ah and others mAh. 1Ah = 1000mAh
It is quite safe to use a battery with a lower or higher Ah / mAh rating. However it may affect how long your device lasts on a single charge.