What squeg said
I might add a few comments to his otherwise comprehensive answer. The reason his sync data files are as big as they are is because he probably has the option to save the last feed for each channel turned on. If you're only looking to backup your Awasu, you can turn this off which will produce significantly smaller sync data files. It'll be much faster as well
Saving sync data won't save any plugin scripts or XSLT's or anything else that you may have manually installed so for a complete backup, you need to also save the Awasu installation directory.
In fact, if you're only looking to back things up, a simple save (and restore, if necessary) of the Awasu installation directory is sufficient. Some stuff is stored in the Registry but none of it is critical; everything of importance is stored in data files in the installation directory.