You're not being stupid... no question is ever stupid. Unless you ask why no question is ever stupid. Then you're a moron (jk).
The hypercube you see is a 3d representation of the four dimensional object. See the lines connecting the two cubes? Those are actually moving along the fourth axis, but since we can only allow for three in our world, we draw it moving diagonal. The inner cube and the outer cube on on different "cells". For example, think of a 3d cube. The square on top is on a different plane then the square on the bottom.
If we draw a 2d representation of a cube, we would get a square within a square, with the vertices connected. The inner square would be on the bottom of the cube, whereas the outer square would be on top. In reality, however, both squares are equal size.
That's probably confusing. I'll post some pics in a minute.
Update:
This picture is a cube, when viewed top-down. It's the 2 dimensional picture of a cube, with one of the sides shaded purple. Notice that the side is a trapezoid, when in reality it is a perfect square. Notice that the face farthest away from you is smaller than the one closest to you. These are distortions you get when you flatten an object. The hypercube you see with a cube within a cube is a hypercube flattened, so there will be distortions; the inner cube is smaller, when in reality it is the same size, and lies in a cell farther away from you four-dimensionally. You also get the "trapezoids" (except their actually prisms now, with one of the bases smaller than the other), that are actually supposed to be perfect cubes, but once again, their distorted as well.
Update #2:
Here's a picture of a hypercube, jacked from
this site, except I added the purple fill-in, to highlight one of the "trapezoid" prisms, for clarity.