Double check is the most forcing move in chess because it eliminates two of the three normal responses to check. Since two pieces are giving check at once, capturing one attacker still leaves the king in check from the other, and interposing a piece can block only one line of attack. The king must move, which severely limits the defender's options.
This makes double check devastatingly effective in tactical combinations. Even if both checking pieces are unprotected or can be captured, the defender cannot take either one because only a king move is legal. Many famous combinations involve a double check that drives the king to a fatal square.
Double checks arise naturally from discovered attack setups and are a key ingredient in many mating patterns. When you have a discovered check available, always consider whether the moving piece can give check as well, since double check often leads to forced checkmate sequences.