A pin is a situation in the game of chess wherein a piece must remain in its current position to prevent the capture of a more powerful piece behind it. This type of force is most effective when the pinned piece is protecting a king, an absolute pin.
For example, see the position to the right. Black's king resides on its starting square, e8. A Black knight on e6. White has played rook to e1, threatening to take the knight. This prevents Black from bringing his knight further into play, by pinning it to the king. Moving it would be an illegal move.
Pinning, as can be seen from the diagram, can be put to good use removing a piece (usually defending) as a factor in the game, until the piece behind it has been moved, generally the king. So, the pawn on g5 having previously been defended by black's Knight is now undefended, as the Knight could no longer retake without breaking the rules of the game.
Note however that relative pins, in which the piece behind the pinned piece is not the king, must be considered carefully for tactical soundness. As it remains legal for the pinned piece to move, although at material cost, in some cases a surprise sacrifice is possible that can completely turn the tables on the player who relied on the pin. The Legal sacrifice is a famous example of such a pin-breaking maneuver.
Only queens, rooks, and bishops can pin a piece, due to the knight's ability to move over other pieces. Pawns and kings cannot simply because they can't move far enough that they would be able to threaten a piece more than one square away.
See also: skewer.