The gobbledygook is not meant to be human-readable.
It's intended to be concealed by the PGP plug-in in your mail client, which then simply gives you a green banner at the top of the message saying it has a valid signature from Kim or me or whoever.
Same as an attachment: If you look at an attachment in plain-text, it's gobbledygook too. But most sensible mail clients hide that and simply present is as a pretty attchment to the user.
The gobbledygook is proof the mail actually came from us, not an imposter; and that is has not been altered in any way.
The boring technical stuff:
The signature is digest ( a one-way hash function ) of the content of the mail, which is then encrypted with our secret private keys. This can be decrypted by the recipient's PGP plugin, using the sender's public key, which can be grabbed from the public key-servers where we put them. If the recieved digest decrypted with the sender's public key matches the message digest we compute ourselves, then we know the message has not been altered of faked.
The Bad Guys can't pretend to be us, since they don't know our private keys.
So they can't fake or alter a message, since they can't re-sign it.
When I send a signed message, I need to provide a pass-phrase which protects my private key, so no-one using my PC can send a message signed by me.