Quick Parry is a passive skill that gives the player the ability to inturrupt their weapon attack mid-animation with a bullet soul (UP + B). It only works while standing.
It is generally more useful with slow weapons.
It's game description, "Deflect normal attacks by pressing UP + B." is a mistranslation. It should read, "Inturrupt normal attacks by pressing UP + B.".
Soma Cruz is able to use this ability with Yellow Souls in Castlevania: Aria of Sorrow,. It can be obtained with a Dead Warrior soul.