Illumos is not intended to be a fork of the OpenSolaris operating system itself and distributed as a binary distribution (like what "Project Indiana" emerged as a binary distro when Ian Murdock joined Sun Microsystems a few years back) but a base for other vendors to build upon. While there are not as many OpenSolaris distributions as there are Linux distributions, the Solaris world has Nexenta, the Nexenta-based StormOS, BeleniX, SchilliX, and a couple others. Should any of these projects lose faith in Oracle or the OpenSolaris code-base were to disappear, they can switch to using Illumos.
The major goals for the Illumos project are to be a self-hosting SunOS derivative, to be fully open-source, maintain 100% ABI compatibility with Solaris, legally usable by upstream, no corporate dependencies, and to be a basis for other OpenSolaris distributions. Illumos is initially targeting x86 and x86_64 (amd64) support while SPARC support should be here "really soon" according to their press slides.
What the dozen or so developers working on Illumos have accomplished so far is replacing some of the closed-source bits of OpenSolaris with their own open-source replacements (contrary to the name, OpenSolaris is not fully open-source). Among the parts of the OpenSolaris stack they have replaced with their own open-source solutions have been the closed bits in libc, critical closed-source utilities, and some drivers. Illumos currently boots, but a few closed-source bits still need to be replaced.
Coming up soon the Illumos developers plan to work on a NFS/CIFS lock manager, full kcf module/daemon (the crypto framework), trusted extensions, many more drivers, and further dependency resolution.
Illumos hopes to be the truly open-source OpenSolaris that is maintained by the community and not dependent upon a corporation (though Illumos is currently sponsored and worked on by Nexenta developers) that Nexenta and other OpenSolaris distributions can use when building up their operating system. Illumos hopes to not be a competitor to Oracle OpenSolaris but rather collaborate and contribute upstream, but if Oracle does decide to further disregard the OpenSolaris community, there is now an alternative.
More on this project can be found at Illumos.org.