refers to a battery's discharge current over time. Usually measured against a 20 hour period, Ah is used to determine battery current capacity. It determines the length of time a current can be drawn, not how quickly current is drawn. Here's an example: the Casil CA1240 is a 12 Volt, 4AH battery. This means 0.2 amps (4Ah / 20hrs) of power can be constantly drawn over a 20 hour period before the battery is completely depleted. Battery capacity can be affected by a number of outside forces, such as temperature and how deep the battery has been discharged.
"mAh" (milli-ampere hour)...
also measures how much constant current can be drawn before a battery is dead (like Ah). The only difference is mAh is typically measured over a one hour time period. A battery with 2500 milli-amps (aka: 2.5 amps) can support a current draw of 2500 milli-amps for one hour. Batteries with higher mAh ratings tend to be bigger and heavier.