How do rear stabilizer bushes on a 2003 Ford Focus sedan work?

They're just a simple rubber bushing around the stabilizer bar and clamped into place. They allow the stabilizer bar (or swaybar or anti-sway bar as you might also call it) to pivot and bend slightly as you drive over uneven road surfaces and as you corner.

If you choose to replace them (usually because they make a clunking noise over bumps) it is easiest to do so with the endlinks disconnected. Otherwise, be exceptionally careful not to bend the clamps when installing the new bushings.