From the Super Mario Wiki
“Hey, I think I just warped! That sure was a fast trip!”
—Mario, Fortune Street
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.
It returns in Mario Party: Island Tour, with the same purpose. It appears only in Rocket Road.