Being web based and open source has made it the bug tracking tool of choice for many open source projects, and quite a few commercial ones.
Bugzilla relies on an installed HTTP server (such as Apache) and a database (usually MySQL) to perform its work. Bugs can be submitted by anybody, and will be assigned to a particular developer. Various status updates for each bug are allowed, together with user notes and bug examples.
The notion of a bug in bugzilla is very general; for instance, it can be used to track feature requests as well.