It basically means that a module that would normally handle an IIS feature is not working in some way. Obviously, it might not be installed, but it is more likely that it has been broken by an upgrade. IIRC, if the module is not installed at all, you get a different error.
The event log has the same error plus another equally unhelpful one: "Trace provider or tracing area name 'WWW Server' is not recognized. Check the
Anyway, a quick Google search and I decided to uninstall URL Rewrite (which I assumed was the module that was likely to be the problem) and then reinstall it via the Web Platform installer.
After doing only that module and without a restart, the site now loads!