Currently (1.0.1), the database is saved each time one of the "Mark as..." scripts finishes and (as a precaution) when the application exits. You can save the database manually (e. g. if you have accidentally removed the files and fear that the application might crash) from the "File" menu, but the "Save" menu entry is there mostly for future fine-grained control.
The databases reside in <your home directory>/Library/Application Support/JunkBroom. The files are called
The numbers file simply stores the number of messages processed (for legitimate and junk messages), which is a vital part of the calculations.
The files can be viewed using the plist editor (which comes with the Developer Tools), but note that if they are large, the editor will choke.
If you have been using the "Backup" menu entry, all those files will exist twice, their second incarnations with a ".bak" added to the end of them.
If you have been using a version older than 0.91, you will also have a file called "dictionaries" that you can safely delete (it contains the databases in old-style format) if you have already run the newer version.