OpenXDK is a free and open source development kit for the original Microsoft Xbox. It is aimed at developers of homebrew software and released under the GNU General Public License version 2.0 (GPLv2). The project was originally started in 2002 by Aaron Robinson (caustik), who was later joined by others, most notably Craig Edwards.
OpenXDK was written from scratch and aimed to be a replacement for the official Microsoft XDK that was widely used in the Xbox homebrew scene, despite this unlicensed usage being legal limbo at best. Due to this questionable legality, most Xbox homebrew software could not be distributed freely and was only available at certain places.
Contrary to that, software developed using the OpenXDK is completely free of proprietary code and is thus fully legal, allowing a much easier distribution.
OpenXDK might not be on par with the official Microsoft XDK and the number of applications using it is only a small percentage of the large pool of Xbox homebrew software. This is largely because OpenXDK only reached maturity after the Xbox scene had already reached its peak. It was nonetheless used by a number of applications, emulators and games and can be a good alternative if you plan to start a new homebrew project.