If battery is a voltage source then why current is mentioned ? The current depends on the resistance in the circuit right? Then how can a battery give mAh as well as voltage?
mAh is a measure of battery capacity, not instantaneous current. A 1000mAh battery can theoretically sustain a draw of 1000mA for one hour before it runs out. Broadly speaking, that means it could also sustain a draw of 500mA for two hours, or 2000mA for half an hour, but in reality battery capacity varies somewhat depending on how much current you draw; lead acid batteries, for instance, have significantly more capacity if discharged slowly.
The product of a battery's mAh rating and its voltage gives a rough approximation of power capacity (in watt hours) - rough, because a battery's voltage will also vary during the discharge cycle.