Piercing (貫通, kantsū) is battle damage that originates from a card effect and is characterized formally by the following 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. This lore has now changed to If this card attacks a Defense Position monster, inflict piercing Battle Damage to your opponent. after the release of Problem-Solving Card Text. In one instance 'This card inflicts Piercing damage.' was printed on "Cyberdark Horn". Cards printed with similar effects in future sets and even the same set have not used this wording, until the release of the new wording.
Example: Player A's "Dark Driceratops" (ATK 2400) attacks Player B's Defense Position "Mystical Elf" (DEF 2000). Regardless if "Mystical Elf" is destroyed or not, Player B takes the difference (400 points in this case) as damage.
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 yourSpell Card, and thus it's your opponent — not you — who takes the extra damage, due to the wording on the cards.
Also there are effects that would give momentarily piercing effect to various monsters. Cards such as Meteorain and Drill Synchron can be used to generate piercing effect while you monster attacks a defense position monster
The following cards automatically have or allow Piercing in OCG and TCG: