The online help describes where Awasu stores your data.
At a minimum, you should backup the contents of your roaming data directory.
You may also want to backup selected parts of your local data directory, although this may increase the size of your backup considerably. Check the notes for details on what each file is used for.
If you want to backup the Awasu software (because you are upgrading it), you should also take a copy of the Awasu installation directory (e.g. C:\Program Files\Awasu\).