Trac is basically an issue tracker and ticketing system, similar in principle to Bugzilla. It is a Python app that runs on the server. A large part of the usefulness stems from one feature: there is a commit hook that is called whenever a commit takes place. This allows parsing the commit message, looking for special commands, and thus automatically marking indicated tickets as closed/fixed.
Workflow is as follows: write up a trac ticket, which is either assigned to someone or accepted by them directly. They can solicit feedback/discussion via comments on that page and use the ticket as a TODO-list (by strikethrough via Wiki formatting of completed items). When committing changes that relate to the ticket, say in the commit message "refs #123". That causes the message to be appended to the ticket as a comment. "closes #123" would do the same and also mark the ticket as closed.
Note that any interested parties (in particular, the ticket owner) can be signed up to receive email notifications whenever the ticket is changed.
This Wiki is also a part of Trac and our intention is that it is and will continue to be a vital source of information. Parts may be outdated, so feel free to help improve it and ask questions about the topics listed if something seems outdated unclear.
One final useful feature is Browse Source. Hit the "View Changes" button on the bottom, replace the top revision number with the desired starting revision, and it'll show a fancy diff of that changeset. Very convenient in meetings to show others what changed, or when you don't have SVN installed.