Explanation

A double check is a check given by two pieces simultaneously. One piece moves and gives check, and also discovers a check from another piece.

It is more difficult for the opponent to defend against a double check than it is to defend against a normal check. There are three ways to defend against a normal check: Capturing the piece that gives check, blocking the check, and escaping with the king to a safe square. Against a double check, it is impossible to capture both pieces giving check with one move. Blocking the two checks with one move is also impossible. Therefore, the only way to defend against a double check is to escape with the king.

Compared with discovered check, where you get a "free" move with the discovering piece, with double check you get that free move as well, but it is also a "you cannot capture me" move with both pieces.

A double check can be used to force the opponent's king to a different square, where checkmate can be delivered immediately or forced within a few moves.

Examples

White can give a double check with Nf7+.
Black is not allowed to block the bishop check with Ng7, nor to capture the knight with Rxf7 or Qxf7, but is forced to move the king to defend against both checks.
The only move is Kg8, and White can checkmate with Nh6#.
This is a common way to achieve dragonfly mate.
Note that Ng6+ would also be double check forcing Kg8, but a bad move as there is no mate.

With the last move ...f5, Black attacked White's queen and probably expected a queen move or en passant capture. However, White can win with the double check Bf6+.
Black is not allowed to capture the queen nor the bishop, and is forced to move the king to defend against both checks. If the king goes to h6, White can checkmate with Bg7#.
And if the king goes to f7, White can checkmate with Qg7#.

Pattern matching

If you can give a discovered check, and also give a check with the discovering piece, it is a double check.
Always look closely at all double checks, as the only defence is to escape with the king.
Even if it is not checkmate immediately, you might be able to checkmate the king or win material anyway.

Related patterns