So, first of all, it only works with RESTORE VERIFYONLY. RESTORE VERIFYONLY does some basic checking on a backup to make sure that it can be read and understood by SQL. Please note, it does not mean that the backup can be restored. It will check things like the checksum, available diskspace (if you specify a location), the header and that the backup set is actually complete and readable. Basically enough to see if it will start restoring, but it could still have errors later on.
As for what LOADHISTORY actually does? It causes you to write an entry to the restore history table. You can tell which record this is because the restore_type is set to a V. Really, the only benefit here (as I see it) is that you can do reporting on what backups you’ve verified.
Click through for a demo.