The fork is a very useful tactic in chess. By definition, a fork is when you attack two or more chess pieces at some time. The advantage of this is that even if your opponent moves one of his/her pieces that is under attack, you can still capture the other chess piece.
In this chess diagram above the white knight on d6 is attacking both the black king on e8 and the black queen on c8. The black player must move the King out of danger and the white knight can then go and capture the queen.
We must remember that not every fork is good. In the chess position above the Knight on e6 is attacking the bishop on f8 and the pawn g7. The pawn is protected, so it is not worth taking with your knight. The bishop is also protected (by the King on e8) and worth the same value as the Knight. The white player would not be able to gain an advantage with this fork, so it is not worth making.
An easy way to remember the fork is by imagining the eating utencil. What makes it unique is that it has multiple prongs, hence a multi-direction attack on the chess board.