[Slick]

mAh = milli-Amp-hours

This is basically the capacity or endurance of the battery. Theoretically, A 2100 mAh battery is rated for putting out 2100 mA for 1 hr or 1 mA for 2100 hrs or anything in between. In practice, these extremes are not encountered and generally a battery will last longer at lower discharge rates.

The device doesn't know/care what the amp-hr rating of the battery is. What does matter is the voltage rating. So long as the voltage rating is the same, the device will draw rated current until the battery is depleted; at which time the output voltage drops significantly. Some "smart" devices will sense the voltage droop characteristics of the battery and give warnings or "charge level" indicators.

edit: same goes for the charger; not a problem. It will charge to full capacity regardless of the rating.

An AC adapter basically converts AC to DC at the required voltage; the device "sees" an infinite battery hooked up, but can't tell the difference between the AC adapter and a battery. That is until you stop paying your electric bill, the next hurricane, etc...