In Super Smash Bros., Master Hand is the final opponent of the 1P Game, acting as a final boss. He resides in the Final Destination. He uses his size and shape to his advantage - he slaps, punches and flicks the player around, but receives no knockback from the player's attacks; all of these trends would be carried over to later games in the series.
Master Hand can't be defeated by normal means; instead, he has 300 HP which must be depleted. Once 0 HP is reached, he explodes into the background while the screen fades to white; after the last results screen of the game, which has its own fanfare, a cutscene plays, showing the player's character turning back into their plush doll form, the camera zooming, then a sudden transition to black, punctuated with the sound of a door closing.
Master Hand first appears in the opening cinematic. He positions inanimate plush doll versions of two random characters on a table, and after carefully positioning everything around them, he counts to three, snaps his fingers, and changes the table into a stage resembling Peach's Castle; additionally, both of the plush dolls spring to life.