Ah is an abbreviation for amp hours. mAh is an abbreviation for milliamp hours (1Ah = 1000mAh). Amp hour ratings define the battery's total capacity. The higher the mAh/Ah rating, the longer your battery can last between charges (this is runtime).
More on Battery Capacity: Battery capacity quanitifes the total amount of energy stored within a battery. More capacity equals longer runtime between battery charges. Battery capacity is measured in amperes, which is the volume of electrons passing through the batteries electrolyte per second. A milliAmp hour (mAh) is the most commonly used notation system for consumer electronic batteries. Note that 1000 mAh is the same as 1 Ah. (Just as 1000mm equals 1 meter). Generally, BatteryShip.com batteries have a mAh rating 30-100% higher than the batteries that are originally installed by the manufacturer of your device. Another way to consider a battery's capacity is by runtime (how long a battery will power a device before the battery is recharged). The higher the capacity the longer the runtime. The longer the runtime the longer you will be able to use your device without recharging the battery. More capacity equals more runtime. More runtime equals better value!