...in Edwin Abbott Abbott's book Flatland, he writes about a square that lives in a two-dimensional world, like the surface of a piece of paper. A three-dimensional being has seemingly god-like powers from the perspective of this square: such as being able to remove objects from a safe without breaking it open (by moving them across the third dimension), see everything that from the two-dimensional perspective is enclosed behind walls, and remaining completely invisible by standing a few inches away in the third dimension. By applying dimensional analogy, one can infer that a four-dimensional being would be capable of similar feats from our three-dimensional perspective. Wikipedia
These are 2 dimensional renderings of rotating tesseracts or hypercubes, 4 dimensional objects that make me feel a bit queasy to look at. Their official description is "a regular convex 4-polytope whose boundary consists of eight cubical cells". I guess something that looks that complicated also needs a complicated description to match.
According to some physicists, there are actually 10, 11 or even 26 dimensions out there. Most of them are too small for us to notice though.