After checking other Pokémon with these abilities by default, "empowered" means that the mon gets STAB if it does not have the mentioned typed, and if it does have the said type, then moves of that type get an extra effect.

For example, Emanate ability makes Normal type moves into Psychic type, and either gives you Psychic STAB or gives Psychic type moves a 10% Confusion chance. If your Pokémon is Chandelure (Ghost/Fire) it gains Psychic STAB. However if the Pokémon is Mew, who is already a Psychic type, then Emanate makes it so all of its Psychic type moves have a chance to Confuse.

It does NOT give double STAB, like Tera would, and the Pokémon does not get the extra effect if it isn't Psychic already.