The Mario Finale is Mario's Final Smash in Super Smash Bros. Brawl for the Wii. Mario is able to perform this attack when he comes in possession of the Smash Ball. When he unleashes it, a mighty barrage of fireballs will be shot from his hands and attack almost every opponent on the screen. As they travel across the stage, they expand vertically, so for maximum effect, you should use the attack from one side of the stage and use it in midair so it spreads and hits everyone.
Changes in later iterations
Super Smash Bros.for 3DS / Wii U
The changes seem predominantly aesthetic, changing the dragons for an explosive flame effect. It deals more damage and traps opponents better. It has lower initial vertical range, but the flames grow faster and larger, resulting in a higher vertical range by the end of Mario's Finale.
Mario with a Smash Ball, unleashing his ultimate attack. The twin dragons of flame he releases wallop all characters in range. The flames spread up and down, so it's best to release them from the edge of the screen at an appropriate height. His flaming eyes are proof of his excitement for this explosive attack.