Excerpts from Wikipedia:

Pretty Good Privacy (PGP) is an encryption program that provides cryptographic privacy and authentication for data communication. PGP is often used for signing, encrypting, and decrypting texts, e-mails, files, directories, and whole disk partitions and to increase the security of e-mail communications.

GNU Privacy Guard (GnuPG or GPG) is a free software replacement for Symantec's PGP cryptographic software suite. GnuPG is compliant with RFC 4880, which is the IETF standards track specification of OpenPGP. Modern versions of PGP and Veridis' Filecrypt are interoperable with GnuPG and other OpenPGP-compliant systems.

 

The Wikipedia article has a good overview of GPG, but you should also read about the Web of Trust.

 

If you upload your public key to jabber.rwth-aachen.de or enter your key's fingerprint to download the public key from a keyserver, all emails from jabber.rwth-aachen.de to you will be signed and encrypted, otherwise they will be sent in cleartext.