STAB (stands for Same-type attack bonus) is a boost in the base power of a move that has the same type as the Pokémon using the move. This boost increases the damage done by 50%. This boost can become 100% instead when a Pokémon has Adaptability as its natural Ability.
For example, a -type Pokémon using a -type move will gain a 50% boost in power for that turn, because the attack is the same type as the Pokémon. STAB does not apply to moves that do a set amount of damage, nor ones that do not use the normal damage formula, such as Dragon Rage and Seismic Toss.
It is possible to receive same-type attack bonus with Hidden Power. So a -type Pokemon using Hidden Power Flying will receive a same-type attack bonus. However, since Hidden Power can never be -type, it is impossible for a pure -type Pokémon to receive STAB when using Hidden Power.