Basically the Xbox is a PC, so standard i386 Linux can run on it. Still there are some small differences, mostly related to protection, that make it somewhat different and require some modifications in Linux.

Of course it is possible to write a Linux distribution for the Xbox from scratch, but as it is so similar to a PC, it makes more sense to just modify an existing distribution to be Xbox compatible. The great thing about it is that an Xbox-enabled boot or installation CD can run both on the Xbox as on the PC. This HOWTO describes how a modified Xbox works and summarizes the steps you need to take as a developer.