Explanation

This is a very common combination. You can think of the blocking piece being pinned to the forking square.

Examples

Black can open the line for the rook from c2 to g2 by exchanging queens with Qxd3.
White has to recapture with the knight, which was blocking the rook.
Black can then win with Rxg2+, forking king and bishop.

Sometimes the opponent's recapturing piece is also lured into the fork, as in the following example:

Black can open the line for the rook from e1 to e1 by exchanging rooks with Rxd1+.
White has to recapture with the knight, which was blocking the rook on e4.
The knight is also lured to d1, where it can now be picked up with the fork Re1+.

Sometimes opening the line can be a temporary sacrifice:

Black can sacrifice a knight with Nf3+!
White has to capture the knight with Rxf3, opening the line for Black's queen from e6 to e1.
Black can then win a rook with the fork Qe1+.
Black has sacrificed a knight, but won a rook, so won the exchange in the end.

Related motifs

A line can also be opened for the fork attack (instead of for the fork move).
It is also possible to open a line for checkmate, or for a capture (use the pin).