What does 1800mAH mean?

This is a measure of battery capacity. It relates to how long a battery can produce a certain amount of current. For example, a fully charged 1500 mAh battery can provide 100mA for 15 hours (or 50 mA for 30 hours or 200 mA for 7.5 hours, etc.) The battery rating is the capacity for a new battery. After many charge/discharge cycles, you will start to see a reduced capacity.

Related note: The capacity of a battery doesn't relate to the maximum current you can draw from the battery - that depends on several factors including the type of battery, its size and construction. For example you might be able to safely draw 15 Amps from a hobby style 1500 mAh Lipo (Lithium Polymer), but don't try to get 15 Amps out of 1500 mAh AA Nicads.