In Pokémon, STAB is an acronym for same-type attack bonus. It means when a Pokémon uses an attack of the same type as itself, the base damage in the attack will be 150% its normal value. For example, if an Umbreon uses the move Bite, which has a base damage of 60, the value used when figuring into the attack would be 60 * 1.5 = 90 because Bite is a Dark-type move and Umbreon is a Dark-type Pokémon. However, if an Umbreon uses Tackle, which has a base damage of 35, then the base damage would remain 35 because Tackle is a Normal-type attack.
Normal type myth
There is a myth that Normal type Pokémon don't get STAB, probably perpetuated because of the way the trading card game treats Colorless Pokémon. This, however, is not true. If a Normal-type Pokémon (Wigglytuff) uses a Normal-type attack (such as Pound, which has a base damage of 40), then STAB is applied (base damage 60).