This command can actually be used inside git repositories that do not use git-annex at all; when used in a repository using git-annex, it does additional repairs of the git-annex branch.
It works by deleting any corrupt objects from the git repository, and retrieving all missing objects it can from the remotes of the repository.
If that is not sufficient to fully recover the repository, it can also reset branches back to commits before the corruption happened, delete branches that are no longer available due to the lost data, and remove any missing files from the index. It will only do this if run with the --force option, since that rewrites history and throws out missing data. Note that the --force option never touches tags, even if they are no longer usable due to missing data.
After running this command, you will probably want to run git fsck to verify it fixed the repository. Note that fsck may still complain about objects referenced by the reflog, or the stash, if they were unable to be recovered. This command does not try to clean up either the reflog or the stash.
It is also a good idea to run git annex fsck --fast after this command, to make sure that the git-annex branch reflects reality.