Link to the Wikipedia definition and examples

Discovered Attack is a tactical trick that happens when a piece is moved away to reveal an attack from another piece hiding behind it. One of the most dangerous varieties of discovered attack is discovered check when we reveal an attack on the King (check). In this latter case safety of the King is the number one concern our opponent has to deal with and so the piece that moves away gains immunity against being captured. Quite often discovered attack can be treated as a form of a double attack since it often creates 2 attacks: piece that moved away and the piece that is revealed.

In the later lessons I will talk about Double Check. When the piece that moves away gives a check as well as the piece that is being discovered.

There is a very well known trap in the French Defense that is a very good illustration of a discovered attack. Follow the game below written in extended (initial and final squares) Algebraic Notation.

1.e2-e4 e7-e6 2.d2-d4 d7-d5 3.e4-e5 c7-c5 4.c2-c3 Nb8-c6 5.Ng1-f3 Qd8-b6 6.Bf1-d3 (looks like white is losing a pawn on d4 (3 attacks, 2defenses)) 6)... c5xd4 7.c3xd4 Nc6xd4?? 8.Nf3xd4 Qb6xd4?

and in this situation we note the opposition of the Queens. White Bishop is the only piece standing in between. When we move the Bishop away Black Queen will be under attack. Where should we move it so that Black has no time to defend their Queen? We should play 9)Bb5!+ Kd8 (defense of the King is priority number one) 10)Qxd4 (winning a free Queen)

In Petrov Defense (other wise known as the Russian Game) there is a devious trap that illustrates the power of discovered check

1.e2-e4 e7-e5 2.Ng1-f3 Ng8-f6 3.Nf3xe5 Nf6xe4? 4.Qd1-e2 Ne4-f6??

let's take a close look at the diagram and note the opposition between the White Queen and Black King. White Knight on e5 is the only piece in between them. So if we move this Knight we will reveal a check from the Queen. No matter where we move it, this Knight is immune from capture. Why? 5.Ne5-c6+ (attacking the most prized piece is the best move) 5)... Qd8-e7 (protecting the King) 6)Nc6xe7 (winning Queen for Knight.

Summary:
Taking advantage of the discovered attack: (example1)

    Piece that moves away to reveal the attack should do so with check, snacking on the enemy's pieces or creating another (double attack) powerful threat.

Taking advantage of the discovered check: (example2)

    Piece the reveals the check "gains immunity" and should use it to attack the most valuable target available.

Defending against discovery:

    Often there is really no good defense. It is best to either minimize the losses by protecting or moving the more valuable piece.
    The only possible attempt to is to create your own attack that is more powerful than opponent's (preferably using attacked piece (move it away with tempo)).