A tesseract is a

hypercube, the

four-dimensional equivalent of a

cube, which has been unfolded into three dimensions.

Since four-dimensional space is difficult for the human mind to visualize, the best way to think of this is to remove a dimension. Every school child has made a cube from a two-dimensional piece of paper by cutting out the following shape:

_____
| |
A| |
_A___|_____|___________
| | | | |
| | | | |
|___ _|_____|__ __|__ __|
| |
| |
|_____|

and folded along the lines to create a three-dimensional cube. This is called the net of the cube. When we fold it up, the edges labelled A, become the same edge in the cube. Similarly, other pairs of edges merge to form one edge in the cube

The three-dimensional 'net' of the tesseract looks like this:

/\ /\ /\
/ \/ \/ \
/ / \ \
|\ |\ /| /|
| \ | \ / | / |
| \| \/ |/ |
\ /\ | /\ /
\/ \ |/ \/
/ \/ \
|\ /\ /|
| \ / |\ / |
| \/ | \/ |
\ | /|\ | /
\| / |/\| /
\/ \/ \/
\ | /
\ |/
\/

*/me realises that representing four-dimensional geometry in ASCII art is probably a mistake*

In case that isn't clear, it is a stack of 4 cubes, with four more cubes arranged in a cross around the second cube from the top. When we 'fold' this up, the top face of the cube at the top of the stack merges with the bottom face of the bottom cube, the adjacent edges of the cubes in the cross join, and so on to form the hypercube.

As a interesting historical note, in the picture Christus Hypercubus, Salvador Dali depicted Christ being crucified on a tesseract.