In what sense is a tesseract (shown) 4-dimensional?

Question

This video and this image show a tesseract, which is a 4d cube:

In what sense is this cube 4 dimensional? Where is time? (commonly called the 4th dimension, although I realize here its probably some sort of direction).

Answer 1

You picture displays a 3-D model of a 4-D object. Time is not one of the dimensions in this case.

Wikipedia has a nice description:

http://en.wikipedia.org/wiki/Tesseract

Answer 2

The tesseract is the four dimensional analog of the cube. It lives in $\mathbb{R}^4$, four dimensional euclidean space. This four dimensional space has all dimensions equivalent, with none of them being special like time. The space is the set of points $(x,y,z,w)$ where the coordinates range over the reals. One of the tesseracts has $16$ vertices, with all combinations of $\pm 1$.