STAB stands for Same Type Attack Bonus, and is the added damage a move of a certain type does if used by a PokéMon of the same type.
Generally, a move's power if STAB as applicable is 1.5 of its power.
For example, a Water-type attack with the base power of 100 used by a water-type PokéMon would have the base power of 150 rather than 100, due to STAB. The same move would not get the +50% benefit if used by a non-water-type PokéMon.