Each player had a single movement piece that went around the perimeter of the board. There was four short sections that went into the middle of the board, but offset, one dedicated to each player. I think there was a couple sections where you could 'slide' your piece, snakes and ladders style. If an opposing piece was on the 'slide ' you would knock them back some squares.
If it's classic, that certainly sounds like Sorry, and if it's more classic, parcheesi. If it's modern, I'd ask questions about theme and art and characters.