This refers to one of two things; A colloquial term to refer to your computer that runs MythTV (usually a combined front-end/back-end). This stems from the common (among geeks, at least) practice of calling a computer a "box". Example: "I just added more ram to my Mythbox."
A python script for XBMC which provides a small subset of frontend functionality. MythBox provides a user interface to MythTV recordings and television as an extension to the popular XBMC (http://xbmc.org/) media software (http://code.google.com/p/mythbox/)