A four dimensional cube. WARNING: Thinking too much about hypercubes may be hazardous to your mental health.

Think about it this way. Picture a square in your mind. Now move to a cube by attaching a line to each corner (or vertex), perpendicular to the two dimensional plane. Fill in the rest, by adding another "square" on top.

Now, without missing a beat, do it again. Add six lines, each perpendicular to three dimensional space. If you didn't stop to think it was impossible, you might have gotten a flash of what a hypercube looks like. Keep trying.