Because the Xbox uses a digital signature system to prevent the public from running unsigned code, one must either use a modchip, or a softmod.
Originally, modchips were the only option; however, it was later demonstrated that the TSOP chip on which the Xbox's BIOS is held may be reflashed.
From the Xbox-Linux home page: The Xbox is a legacy-free PC by Microsoft that consists of an Intel Celeron 733 MHz CPU, an nVidia GeForce 3MX, 64 MB of RAM, a 8/10 GB hard disk, a DVD drive and 10/100 Ethernet.
An Xbox with Linux can be a full desktop computer with mouse and keyboard, a web/email box connected to TV, a server or router or a node in a cluster.
An Xbox with Linux installed can act as a full desktop computer with mouse and keyboard, a web/email box connected to a television, a server, router or a node in a cluster.
This is mainly due to issues with the video chip used in version 1.6 Xboxes that was developed exclusively by Microsoft and which has no source code available at this time.
The Xbox Linux softmod utilizes a save exploit found in the original run of MechAssault, Splinter Cell, 007: Agent Under Fire, and Tony Hawk's Pro Skater 4.