Here's the explaination from Wikipedia...
"An ampere-hour (abbreviated as A·h) is a unit of electric charge. Although it is not a direct measure of the energy in a battery (like the joule (J) or watt-hour (W·h)), it is a common measurement of how long a battery will last (or in the case of a rechargeable battery, how long it will last when fully charged).
One ampere-hour is equal to 3600 coulombs (ampere-seconds), and indicates the amount of electric charge that passes either terminal of the battery when it provides one ampere of current flow for one hour. The commonly seen milliampere-hour (mA·h) is equal to 3.6 coulombs.
However, in reality, the available capacity of a battery depends on the rate at which it is discharged. If a battery is discharged at a relatively high rate, the available capacity will be lower than expected. Therefore, a battery rated at 100 A·h (360000 coulombs) will deliver 20 A (20 coulombs per second) over a 5 hour period, but if it is instead discharged at 50 A (50 coulombs per second), it will run out of charge before the theoretically expected 2 hours. For this reason, a battery capacity rating is always related to an expected discharge time, which is typically 5 or 20 hours.
The relationship between current, discharge time and capacity is expressed by Peukert's law.
In general, the higher the ampere-hour rating, the longer the battery will last for a certain device. Installing batteries with different A·h ratings will not affect the operation of a device rated for a specific voltage."