The public part of Public key encryption.

The idea behind public key encryption is that you have two parts of a key, a public part (which can be given to everyone) and a PrivateKey (which you keep to yourself). If you encrypt something with the public key then it can be only decrypted with the private key, and visa versa. Given the public key, you can't deduce the private key, and usually visa versa (although not always). Thus you publish you public key to the world, and then they can send you encrypted email.

You can "Sign" a document by taking a CryptographicHash of the document, and encrypting that with your private key. Everyone can calculate the hash, and then decrypt the version you gave and verify that they are the same (the document hasn't been modified) and they know that it came from you (since you are the only one that has your private key).

You can then sign other peoples key to say that you verify that it is them. This is known as the WebOfTrust.