There is one master key per database. Poorly named, and has nothing to do with master database.

The master key protects the certificate(s) you use for the backup encryption. You need to backup this certificate(s) and protect that (password, ACL, disk encryption, etc).

During a restore, the certificate is opened and used to decrypt the keys protecting the backup. If the certificate is not available, you can't decrypt the backup.

If you need to restore on the same server, the certificate is there. If you are on a new server, then you restore the certificate on the new server (you'll need a master key there, not the same one, but a master key in the master db) and then restore the db.