File versioning is the ability to backup and recover past versions of files, so you can rollback to a specific point in time. It’s an essential feature, because without it there’s no way to undo changes to files. This would be disastrous if files become corrupted, or if a virus infects them, and these changes are reflected in a backup.
Most online backup services support file versioning, except Pogoplug and MiMedia, so it’s normally not something you have to worry about. Additionally, most backup software supports recovering previous versions of files.