Determining the duration that a battery can power a device
If you look at the units, Amp-hour (capacity of battery) and amps (current draw of device) you can divide the capacity by the load current to get the hours it will run for. This is super naive though, and does not take into account the effect of how large the load current might be (certain battery chemistry do not like high load currents) and temperature effects.

A 2500mAh battery with a 100mAh load current SHOULD last, according to the simple specs given, 25 hours. In reality, depending how the load changes as the battery voltage discharges, the operating temperature, battery manufacturing tolerances etc.. The actual life of the battery may be much less. 

If you have the required life of device and a battery capacity (maybe you've already chosen a battery you want to use?) you can work out a reasonable target (average, maximum) load current estimate by simply dividing the battery capacity by the required working life in hours you want. 

For example: If you have a 5 Amp-hour battery, and you want at least a 24 hour life out of it, 5/24 = 208 milliamps. To be safe I would aim to consume 25% less than the estimated number.