Tapping is a term used in a number of games. Although the exact meaning varies, it is generally refers to using up the resources of some element of the game.

Collectible card games

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In collectible card games such as The Gathering to tap a card means to use it so that it cannot be used again in that player's turn. The visual indication of the tapped status is represented by turning the card 90 degrees to the right.

and the more recent one MTG-New-Tap-Symbol.gif (introduced in The Gathering), 1995).

was filed by Wizards of the Coast to patent the mechanics of some aspects of collectible card games, including tapping.

Mechanics similar to tapping are used in many collectible card games, often involving the same 90 degree card rotation. For example, this act is referred to as setting in Ophidian 2350, while it is known as committing in the Universal Fighting System. A few games, such as the City of Heroes Collectible Card Game, use several different rotational increments (90, 180, and 270 degrees), each denoting a different card status.

MMORPGs

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Tapping is commonly used in MMORPGs as a term for dealing enough damage to a monster or enemy to gain access to its treasure (loot). Usually only one person or group can tap the lootable enemy in question. Once tapped, regardless of who kills the enemy, only the original tapping player(s) can receive the treasure.

Source: World of Warcraft Glossary

Collectible card games | Computer and video game gameplay