A blog post on how the feature works: http://github.com/blog/39-say-hello-to-the-network-graph-visualizer
Here's a use-case:
I've forked project foo. I've been hacking on it for a while and haven't been paying attention to what's been going on in the mainline foo repository. I know that some of my changes have been pulled in, but don't know when that last was. The Network graph would allow me to easily see this.
Similarly, if I maintain project bar, it allows me to see, at a glance, changes in the various forks of my project.
UI doesn't have to be identical, or even similar -- but I've found that those two tasks are quite common and I don't see a good way of accomplishing them in the current UI. If I've missed something, feel free to let me know :)
Bitbucket rules, btw.