The effect of "Piercing" is characterized by the following text in the card lore:

During battle between this attacking card and a Defense Position monster whose DEF is lower than the ATK of this card, inflict the difference as Battle Damage to your opponent.

In one instance this was printed as This card inflicts Piercing damage. on "Cyberdark Horn". Card printed with similar effects in future sets and even the same set have not used this wording.

Although "Piercing" is the official term for this scenario in the context of Yu-Gi-Oh!, in many circles of duelists, Piercing damage is often colloquially referred to instead as "Trample", borrowing from the popular and longer-established Magic: The Gathering card game.

An interesting side-effect of Equip Spell Cards that give Piercing, is that you can inflict damage to your opponent by equipping them to your opponent's monster(s). Then, when your opponent attacks one of your Defense Position monsters with an ATK greater than your monsters DEF, he/she will take the difference. After all, even though it's your opponent's monster, it's your Spell Card, and thus it's your opponent — not you — who takes the extra damage.

The following cards automatically have or give Piercing in OCG and TCG: