Fire Breath is a special attack found in the Super Smash Bros. series. It originated in Super Smash Bros. Melee for the GameCube. Bowser is the only character who is capable of executing this attack, though it should be noted that Kirby can do so if he copies Bowser's ability.
It's a standard B move that'll cause the great behemoth to exhale large bursts of fire. You'll eventually notice that the amount of fire being released from his mouth is decreasing, and momentarily it'll release nothing but harmless smoke. The move was probably inspired by the fact that in the Super Mario series, Bowser is capable of spewing fire from his mouth.