From the Super Mario Wiki
The Minigame Space is a special space found in Mario Party. If a player lands on this space, the player will play a single-player minigame to earn coins for only the player. If the player loses, the player gets nothing.
In Mario Party 3's Duel Mode boards, it appears again, this time with Tumble on it. The minigame Space here works actually the same as the well-known Duel Space: When stopped at it, a Duel minigame begins. Winning the minigame, will let the winner receive 10 coins, freshly coming out Belltop.
Later, it makes an appearance in the Mario Party 6 Solo Mode. When a player lands on this space, he or she will play either a 4-Player minigame, a 1-vs.-3 minigame or a 2-vs.-2 minigame, againts the three different colored Koopa Kids. There is also a space called the Battle Minigame Space, and a Duel Minigame Space. The Duel Minigame Space makes the player challenge a Koopa Kid in a one-on-one battle.