GPG is open source, and is available for every computer system.
I started using Phil Zimmerman's Pretty Good Privacy (PGP) when it was first released.
GPG came a few years later, as the US Fed.Gov was making PGP hard to use (and Phil's life very difficult) due to restrictions on key size and export licensing. Really nasty, if you're interested you can read all about it. Just do a search.
PGP, now GPG, use what is called "Public Key Cryptography", again for in-depth just search. Or go to
http://www.gnupg.org/ for entirely too much information.
What that means is you give away the "Public" key, which anyone can have and use, but which cannot be used to decrypt anything encrypted with itself.
For decrypting, you must use the matching "Private" key.
You could think of them in terms of one-way doors. You can pass through one door using one key, or the other, but you cannot go through the doors both ways (encrypt then decrypt) without BOTH keys.
It's a matter of very difficult mathematics. While it is theoretically possible to generate the "Private" key from the "Public" key, the numbers are so big that it is beyond present computational power to do so.
Watch the movie "Sneakers". The "chip" that everyone is chasing is a code breaker for Pubic Key systems. It's a super mathematical solver that overcomes the problem of breaking the keys. As in the movie, "The Russians use a completely different kind of code" which is true. They didn't rely upon mathematics. The Soviets used "one time pad" encryption, but the pad has to already exist in total secrecy at the other end for such an encryption system to work.
The ability to openly publish the "Public" key is the great befit, because anyone can use the "Public" key but only I can decrypt them.
But take this one step further. Say that I use by "Private" key on a file, called "signing". Then anyone can use my "Public" key to verify that I am the only person who could have signed it.
Combine the two, and you have a message only you could have sent, and only I can read.
Now you know why the US Fed.Gov was so pissed at Phil Zimmerman.