In chess, discovered check is given when the opponents king is placed under attack indirectly by moving a piece or a pawn out of the way of the piece which then delivers check. For example, if White's king is on e1, Black's rook is on e8, and Black's knight is on e4, then any move by the Black knight results in a discovered check on the White king from the Black rook.
+----+----+----+----+----+----+----+----+
| | | | | r | | k | |
+----+----+----+----+----+----+----+----+
| | | | | | | p | p |
+----+----+----+----+----+----+----+----+
| | | | | | | | |
+----+----+----+----+----+----+----+----+
| | | | | | | | |
+----+----+----+----+----+----+----+----+
| | | | | n | | | |
+----+----+----+----+----+----+----+----+
| | | | | | | | |
+----+----+----+----+----+----+----+----+
| | | | | | P | P | P |
+----+----+----+----+----+----+----+----+
| | | | | K | | | R |
+----+----+----+----+----+----+----+----+
Discovered checks are a very powerful tactical device, because the piece the unveils the attack (in this case, the knight) effectively has a free move in which to do as much damage as possible (Ng3+ is best, winning the rook on h1). White has to defend against the check from the rook, and is unable to prevent the knight from capturing any piece it can while this is happening. Effectively, it is the equivalent of making two moves at once, and a wise player will almost never allow themselves to be placed in a discovered check.
Any piece can unveil a discovered check, as the knight does in the above example, but the only pieces capable of giving discovered check are the rook, bishop and queen, the long range pieces. The king and the pawn have short range attacks (1 move in length) and the knight's move cannot be concealed as it has the ability to jump over pieces.