The fact that 2 dimensions have height and width.
3 dimensions have height, width and depth.
Draw a square on a piece of paper. The square will be 2 dimensional (almost) and the paper will be 3 dimensional. If you look at the square, what is the white inside it. It goes out past the square.
Hold a ball and look at it. If that represented the universe and you were inside the ball, you would look at the inner skin of the ball and wonder what's out there even if it is just space.
For space to be finite, it must have some type of wall or boundary somewhere, but then, what is on the other side.