When the ability holder is targeted by a move or targets another with a move, it ignore all stat changes of the opposing Pokémon. This means when the ability holder attacks the opposing Pokémon, any evasion boosts are ignored when calculating if it will hit and it ignores the defense or special defense boosts of the defending Pokémon in damage calculation. It also means when an opposing Pokémon attacks, their accuracy boost are ignored in determining if it will hit and their attack or special attack boosts are ignored in damage calculation.
The effects of Unaware do not affect the effects of the moves; Stored Power, Punishment or Power Trip.