Our main reason to have tests is to ensure we do not loose existing functionality when adding new functionality. Another reason, hopefully getting less important, is to figure out what influences bugs had, respectively what is influenced by a bugfix.
The following list is not complete and likely never will. It is more to give you an idea, what could be tested:
The tests are automatically run every night. When you log in on matsim.org, you'll find a link in the left navigation area ("developer info") where you can look at the nightly status of the tests. If errors or failures occur, an email is sent to Marcel Rieser who will then inform people as necessary.