Ah stands for Ampere hours. It is a measure of capacity, how much electricity the battery can hold.
Eg: A 12 volt 5 Ah battery can deliver 12v at 5 amps for 1 hour. Or 12v at 0.5 amps for 10 hours and so on.
Remember. Voltage is supplied by the battery but current/ amps are drawn by the appliance. Power in watts is calculated as volts x amps. So for instance a 12 volt bulb drawing 2 amps is: 12x2=24 so it is a 24 watt bulb. so on a 12v 5ah battery it will burn for about 2.5 hours. This is why car batteries are quite big for only a 12 volt battery, the massive current drawn by just turning the engine would flatten a small battery, and probably still wouldn't start even then.