Restoring or recovering?

A DB will go restoring if someone runs BACKUP LOG ... WITH NORECOVERY or runs a restore over the database and specifies NORECOVERY. In either case running RESTORE DATABASE <db name> WITH RECOVERY will bring it back online. Can also happen if someone starts a restore and stops the restore part way through (perhaps realising they were restoring over the wrong DB)

A database will go into the recovering state if SQL is restarted and that DB was not cleanly shut down. It's a temporary state, once recovery has completed the DB will come online.