A Trap Card, at its simplest, is a card that activates not upon being played, but once a certain action is taken or criterion is met. Such cards may be placed face down, such as in Yu-Gi-Oh!, played straight from the hand, or even can be played normally with secondary effects that only activate in the previously mentioned manners. Trap Cards are usually used to head off or prevent an anticipated action, such as blocking cards that take away turns, discarding a player's hand for attacking a certain player, or really anything the creator imagines.
Compare Combination Card.
Here are some examples:
TNT: "Lose 5000 points when BUTTON card is played"
Useful Piggy: "Lose 50 points when a Useless Card is played"
Object Of Worship: "Apply this to a card. If anything happens to the card, the person who did it loses a trillion points"