From the Super Mario Wiki
Professor Fungi is a Toad professor in Mario Party 2. He can be found in Option Lab and can be seen typing the player's records on his typewriter (Or Computer as it's called in the game). The records Professor Fungi wrote contain how many times the player played the game-boards in the game, how many times the characters won, minigame records that the characters will attempt to beat the record in the minigame, and Driver's Ed records when the player unlocks the minigame as the player can attempt to beat the record when playing the minigame.
He also has an assistant that has a garbage can next to him. If the player wants to delete the player's save file, Professor Fungi will throw the player's records in the trash can.