The English used in this article may not be easy for everybody to understand. (October 2011)
A tesseract is a four-dimensional object, much like a cube is a three-dimensional object. A square has two dimensions. You can make a cube from six squares. A cube has three dimensions. The tesseract is made in the same way, but in four dimensions, so it looks different from what a person might expect.
The tesseract has eight cells; each cell is a cube. The tesseract is one of the six convex regular 4-polytopes. Unlike three-dimensional objects which rotate on both an axis and a plane (the plane being of length and width and the axis being of the leftover dimension, height), a tesseract rotates on two planes, one made up of length and width, and one made up of height and the fourth dimension. It is the simplest hypercube.