git annex sync or using the assistant involves merging
changes from elsewhere into your repository's currently checked out branch.
This could lead to a merge conflict, perhaps because the same file
got changed in two different ways. A nice feature is that these
merge conflicts are automatically resolved, rather than leaving
git in the middle of a conflicted merge, which would prevent further
syncing from happening.
When a conflict occurs, there will be several messages printed about the merge conflict, and the file that has the merge conflict will be renamed, with ".variant-XXX" tacked onto it. So if there are two versions of file foo, you might end up with "foo.variant-AAA" and "foo.variant-BBB". It's then up to you to decide what to do with these two files. Perhaps you can manually combine them back into a single file. Or perhaps you choose to rename them to better names and keep two versions, or delete one version you don't want.
The "AAA" and "BBB" in the above example are essentially arbitrary (technically they are the MD5 checksum of the key). The automatic merge conflict resolution is designed so that if two or more repositories both get a merge conflict, and resolve it, the resolved repositories will not themselves conflict. This is why it doesn't use something nicer, like perhaps the name of the remote that the file came from.