A Mandelbox is a particular kind of fractal.
You probably have heard about fractals -- "self-similar" objects where, no matter how closely you look at it, it still looks the same. The simplest is perhaps the Koch curve (although this picture is only 3-rd order and how not been divided infinitely many times, as a real fractal is):
Fractals were discovered by Benoit Mandelbrot sometime in the 1970s, and they have truly become useful in science. (I heard Mandelbrot speak a few times, and he is one of the most arrogant people I've ever encountered. Maybe only Lubos Motl tops him.)
Anyway, a famous fractal is the "Mandelbox" - the generation instructions are here
2d Mandelbox fold from Tom Lowe on Vimeo.
Some clever people have created various videos form the point of view of somone flying through a 3-dimensional Mandelbox, and they're pretty amazing:
This one might be the best: