Your private encryption key only can be used to decrypt the messages sent to you. Anyone with your public key can create a message to you. Without the signature

Your private encryption key only can be used to decrypt the messages sent to you. Anyone with your public key can create a message to you. Without the signature there is actually no cryptographic proof that you created a particular message. The really interesting thing about the PGP case is that you can do this and still insure that no one does a MITM attack on your messages. The encryption key is signed by the signature key (identity). So you can verify the identity but still leave no identity laying around.