How does this work? I assume all encrypted emails require both parties use the software, right? So, all my friends, associates, coworkers have to have GPGMail to read my encrypted emails?
GPGMail uses a very well known and white spread technology OpenPGP as its base.
Everyone you want to use it with has to have a mail client which supports OpenPGP in one form or another, but there are many plugins out there, who add support for your favorite mail clients on windows and linux.
It's a typical crypto add-on for a mail client, yes: you can only exchange encrypted mail with other folks who can use PGP. That's pretty much how crypto works.
But to be clear, this is just an interface to the MacGPG backend, so it's not some proprietary format. Your friends, etc. don't need to use GPGMail in particular; any PGP implementation will be fine.
GPG uses asymmetric keypairs for encryption. You generate (at the same time), two different keys: a private key and a public key. The private key is your identity, which you can use to sign outgoing messages, and decrypt incoming messages. The public key, you share to your associates can be used to verify your signature, or encrypt messages only meant for you.
With asymmetricity, the public key is a key which can only encrypt the message, but even the sender cannot decrypt that same message again with that key. Only the single unshared private key can decrypt them.
This ofcourse means that all parties must have their own key pair, and the public keys have been shared between them. Also they must use a GPG compliant program to encrypt/decrypt or sign and verify the messages.
