From the Super Mario Wiki
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Star Spaces are spaces that appear in the Mario Party series, where if a character passes by one, the host of the Mario Party game asks the character who passes by the space if the player will trade 20 coins for a star-*like "Will you trade 20 coins for a star?"* (giving them a "Yes" or "No" answer). The character can say "Yes" or "No" and the character can either get a Star or not depending on the choice.
After the character gets the star, the Star Space moves to a different location in the map. On certain boards, such as Faire Square from Mario Party 6, and DK's Stone Statue from Mario Party DS, the Star Space's location remains stationary. It is called a Star Splurge Space in the DS game.
Although it is impossible to actually land on Star Space, there is a small chance that a new Star Space will appear directly where a character is standing. However, this character is unable to buy the Star if the Star is on the current space where he or she is standing.
When characters pass a star space, they can buy it if they have enough coins. How many coins they have to trade depends on the board. Traditionally, they have to trade 20 coins for a star, but on certain boards, the star may cost as little as five coins or as much as 40.
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