PGP ("Pretty Good Privacy", an understatement) allows you to send and receive e-mails with maximum privacy and security. Unlike the usual transport layer security GMX PGP takes you in charge. You encrypt and decrypt your e-mails yourself. Thus, your e-mails remain confidential, even if your recipient cannot use transport layer security.
Each PGP user has two keys (big files with randomized content), a public (available to all contacts) and a private one (kept secret and available to none but oneself). To encrypt an e-mail, the recipient's public key is used, and can only be decrypted with his private key.
Until now, PGP was hard to use and required advanced IT knowledge. GMX allows you to use this technology more easily and adds some features like usage on multiple devices or cloud based backup. Setting up PGP will take only a few minutes.
End to end encryption requires all algorithms to be performed locally on your own device (and not some remote server you can't control). This is handled by a browser addon called Mailvelope.
PGP offers an additional layer of security independent of usual transport layer security.
PGP usage is not limited to GMX customers. All you need is the recipient's public key.
To use PGP, you'll need either Mozilla Firefox or Google Chrome as a browser. Your contacts need to use PGP as well, GMX PGP or any other implementation.
You will also need access to the recipient's public key. If he or she uses GMX PGP, the public key will be retrieved automatically.
Please note: This section is just a short summary of a complex mathematical concept. For a more verbose explanation, see the Wikipedia article on PGP.
PGP uses a mathematical one-way function to create the keys: Two very high randomly selected prime numbers are multiplied, which is no problem for any modern computer.
It is way harder to calculate the original two prime numbers from their prodct. This step would be necessary to "guess" a private key. If the prime numbers are high enough (and they are!), it is impossible to do so, even with modern super computers.