Explanation

If you capture a piece that is protected by a pinned piece, the capture will force the protector to move out of the pin, and you can win the piece that is exposed behind the protector. This is best explained with a diagram:

In the first diagram, the white rook is pinning the black pawn against the king. White’s queen can capture the knight, as indicated by the arrow. The pinned pawn can’t recapture, because this would open the file and expose the king to a check by the rook.

In the second diagram, the rook is pinning the pawn against the queen. White can capture the black rook with the other white rook, as indicated by the arrow. The pawn can recapture, but this opens the file and exposes the black queen to be captured.

In the third diagram, the white rook is again pinning the black pawn against the queen. White can win the knight with a temporary queen sacrifice, as indicated by the arrow. If Black accepts the sacrifice and recaptures the queen with the pawn, the file opens and the black queen is exposed to be captured by the rook. White regains the queen and has won a knight in the process.

In the fourth diagram, there is no direct capture. White can still exploit the pin and play the knight fork indicated by the arrow. Again, if Black accepts the temporary sacrifice and captures the knight with the pawn, the file opens and the rook can capture the black queen.

Examples

The black knight on b4 is protected by the knight on c6, which is pinned by the white bishop on f3 against the unprotected bishop b7.
White can use the pin to win material with 1.Nxb4.
If black recaptures with 1...Nxb4, White can win the exposed bishop with 2.Bxb7.

Sometimes using the pin can involve a temporary sacrifice, as in the following example:

Black can win with 1...Qxe6!, because the d-pawn is pinned. If 2.dxe6, then 2...Bxf3 3.gxf3 and Black has won the exchange. The intermediate check 2.Qh5+ can be defended with 2...Qh6, blocking the check and bringing the queen to safety.

How to spot a pin that can be exploited

If you have pinned a piece or a pawn, always check whether the pinned piece or pawn is defending another piece or a square that you can use. If so, consider ways to capture the piece, or moves to the square, including temporary sacrifices.