The whole thing about signing a public key with a private key is useful when you have a dedicated key-pair that you use only for signing, and then other key-pairs that you use for encrypting. This dedicated key-pair is your "trusted" key-pair that is somehow known to be legitimately attached to you (often by having it signed by a certificate authority or by having many trusted people sign that they have verified it's connection to you.)
You use this "trusted" private key to sign your not-quite-as-trusted public key. This way, people can un-sign/decrypt your new public-key with your trusted public-key. This is only mathematically possible if it was signed by your trusted private-key.
This process helps people to be sure that this new public-key actually belongs to you.