Reading through the Microsoft Research paper on Gazelle, it becomes clear that it is an intricate beast. It relies on a "browser kernel", 5000 lines of C# code, that exposes the underlying system to webpages using a set of system calls. Web content does not interact with the actual operating system at all; all communication goes through the sandboxed browser kernel. The browser kernel takes care of all resource protection and sharing.
In addition, Gazelle takes the multi-process approach used by Google's Chrome and Internet Explorer 8 a few steps further by not only running each tab or webpage in a separate process, but by also giving separate parts of each website their own process. The authors of Gazelle believe the model introduced by Chrome isn't sufficient. "This granularity [in Chrome and IE8] is insufficient since a user may browse multiple mutually distrusting sites in a single tab, and a web page may contain an iframe with content from an untrusted site (e.g., ads)," they explain. They go even further by considering content coming from "ad.iloveponies.com" to be separate from "user.iloveponies.com". Plug-ins are also run in separate, sand-boxed processes, so that if they go bad, they only affect that particular sandboxed plug-in process.
Currently, Gazelle is built with some additional IE bits on top, and is not production ready. Still, it renders most websites correctly, but there is an additional performance overhead thanks to the IE bits. The authors also state that they have made no concessions to backwards compatibility in favour of security.
JCXP now claims that Gazelle will be the basis for Microsoft's next web browser, which won't sport the IE name, but there's no source. Whether or not this is true remains to be seen; when news of Singularity came out, the entire web automatically assumed that this Microsoft Research project would be the next Windows. Still, the ideas behind Gazelle are sound, and don't sound too far-fetched to be implemented.