Discovered Attacks
A discovered attack happens when a sliding piece (bishop, rook, or queen) has one of its own pieces sitting in front of it, blocking its own attack -- and moving that blocking piece out of the way "discovers" the attack behind it. The piece that actually moves doesn't even need to do anything special itself; the real damage comes from the piece it was screening.
This is what makes discovered attacks so dangerous: the moving piece gets to make its own threat AND unleash a second, completely separate threat from the piece behind it, all in one move. The defender often can't deal with both at once. The most feared version is a discovered check, where the revealed attack is check on the enemy king -- the moving piece is then free to do almost anything it wants (capture a piece, deliver its own threat) since the opponent's king is in check and must respond to that first.
To spot these, look at your own sliding pieces and ask: is one of my own pieces currently blocking this piece's view of something valuable? If so, that blocking piece has a hidden second job every time it moves.
Worked examples
Discovered attack behind a knight screen
Moving the d5 knight off the d-file reveals the d1 rook's attack on the king on d8.
Discovered check behind an own-side knight
White's own knight on e2 currently blocks the e1 rook's view of the king on e8 -- moving the knight off the e-file discovers check.
Test yourself
Click the piece that's currently blocking your own rook's attack.