When you get down to it, it's a unit of
electric charge. It is short for "milliamp hours". It is a unit usually used to describe the
capacity of a
battery. For example a
AA size
NiCad battery might be rated at 600 mAh. This means that it can supply a
current of 600 milliamps for a period of one hour.
However, using some simple maths and knowing a few laws of physics, means that such a battery can supply a current of 1200 mA for a period of half an hour, or 300 mA for a period of two hours.
Generally, the higher the mAh, the better (and likely more expensive and physically larger) the battery is. In particular, it's easy to get more mAh by simply increasing the battery size; eg a "C" size rechargeable NiCad might be 1200 mAh; but getting more mA h into the same size battery is a real challenge.
Also, it's interesting to note that the "mAh" is a unit made to allow people to reason more conveniently. It's not an SI unit for charge, which is of course, the coulomb. It's not too hard to show that 1 milliamp hour is 3.6 coulombs; but if you told someone their battery had a capacity of 2000 coulombs, they'd give you a strange look, compared saying to 600 mAh.