The parry, many times referred to as the catch (although they are two different things), is nothing more than a slight wave of the hand. It is used as a defensive move against straight punches, usually at mid-range. The majority of the time the parry is used against the jab.
To execute a parry, get into the on guard position (in a real boxing match, your position will vary). Then with the rear hand, slap the opponent’s fist (though it may have to be the forearm depending on distance) just before it reaches your face. Slap horizontally from right to left (orthodox stance) or left to right (southpaw stance). There is a slight downward motion, but avoid exaggerating the downward motion and do not go beyond the opposite side of your face. You don’t want your opponent’s punch to get tangled up with your other arm.