Well, it's not a distribution like Ubuntu, etc. Most distributions are targeted to desktop or server machines. There are only a few distributions targeted at embedded devices, though they're becoming more common.
The main reason is the the processors used in modern embedded devices are what are called "systems on a chip", or "SOCs" and they're all different. That means that each Linux is typically very custom for the specific processor. In addition, these devices are typically short of storage, so the Linux is often optimized with unnecessary pieces removed. The chumby is unusual in that it includes a lot of software (device drivers, etc) in the Linux that works with hardware that can be added.
We actually include different versions of Linux for each of the general types of devices - the Linux in the Chumby Classic is different than the Linux in the Chumby One and Insignia 3.5. The Linux we use for any given devices is typically provided by the chipmaker and we tailor it for our specific devices.
You can find the source code to the various flavors of Linux (as well as the various other bits of software we include) here.