TestSwarm is still in alpha and hasn't been added to the Mozilla Labs home page yet.
For developers, TestSwarm currently supports 7 operating systems, ranging from Windows 2000 to OS X 10.5. The project runs its tests on all the major browsers. Whenever an error occurs in a specific browser, TestSwarm will return detailed data about what exactly went wrong.
In the long run, the team plans to make it easier for developers to test their own code on Mozilla's TestSwarm architecture as well. The team also plans to give developers the option to run manual tests, where user interaction is needed.
How to Participate
If you want to help out, just head over to the TestSwarm site. If your browser is needed, a box with an invitation to join the project will appear. Just keep TestSwarm running in a tab and it will automatically ping the project's servers for new tests every 30 seconds.
You can find more details about how TestSwarm works in this screencast: