From the Super Mario Wiki
The Warp Space is a special space that first appeared in Mario Party 4. When one of the players in the gameboard steps in that space, a spinner on the screen appears with the three other opponents' faces and then the arrow starts spinning. When it stops on one of them, the space springs the player to the space the chosen opponent's on.
Warp Spaces returns in Mario Party: Island Tour, where they serve the same purpose. They only appear on the board Rocket Road. In this game, they take the appearance of an Event Space with a worm hole underneath them.