Let's say that your knight is the only piece between your rook
and your opponent's king.
By moving the knight, you've "discovered" a threat by your rook and should announce, p>"Check."
This is an example of a discovered attack.
They are effective when not checking, too,
because often times the other player will be focused on the
piece you just moved, unaware of any threat you just uncovered.
You can discover a threat by moving a piece out of the way of a
queen, rook, or bishop, and the piece that moves may have
some attacking of its own to do.
As always, be on the lookout for your opponent to do the same to you.