An interesting point of this is that 2d man is able to see a shadow of a 3d object - say a cube. He can see the shadow of this cube in his 2d world, but is unable to comprehend what it is.
If you have a 1 dimensional world (ie, a line), and the only movement is "Left-Right" - then the way to turn that 1D line into a 2d square is to project the sides into the 2nd dimension and join the points. Now you have a 2d square.
Doing that again, you can make this 2d square into a 3d cube, again by projecting the corners into the 3rd dimension , and violla, a cube.
Now - we live in a 3D universe. To make a 4D object, all we do is project the corners of the cube into the 4th dimension (which we understand as much as the 2D Flatland man understands the concept of a 3D cube). BUT..
..in the same way the 3D man can see the shadow projected by a 3D cube, so us 3D citizens can see the "shadow" projected by the 4D equivelent - and it's called a "tesseract" I think, and it's as real a shape as the cube is to the 2D man. Here is what the shadow of a 4D object in 3D space looks like..
http://www.logic-alphabet.net/tesseract.htm
I'm sure someone can do a better job of explaining the 3D/4D type stuff, but it's very interesting if you get into it.
Ringo