From the Super Mario Wiki
Tumble is the character that replaces Toad as the host of minigames in Mario Party 3. His appearance is actually very similar to that of a Toad, but he wears gloves and has a die on his head instead of a mushroom cap. He also happens to have no arms, legs, or even a body.
In addition to explaining minigames and controls and getting a Battle Royal or Duel Board started, Tumble will also show the players the new location of the Millennium Star each time it is moved. He (along with the Millennium Star himself) also gives out Star Stamps whenever a player has won at a board.
At the end of the game, the top of Tumble's dice cap opens to reveal the real Millennium Star.
Tumble re-appears as the host of the Shroom City mode in Mario Party Advance. He is also said to be one of Shroom City's guides; he kept this role by the end of the game (which describes him as a "beloved Shroom guide"). Tumble actually did little other than the average host-type things in Mario Party Advance; other than this, though, he can be summoned by landing on a Mushroom Space, which will randomly trigger an appearance of either him or Koopa Kid. Tumble's Mushroom Space-related role shows him to be much more merciful than Koopa Kid, who will take a Mushroom away if a minigame is lost and will give the player one if it's won. He will give the player two Mushrooms if they win and none if the player loses.