Also known as PKI (public key infrastructure). PKI is an encryption system that uses two keys, a public key and a private key. The two keys are known as a Key Pair.
The Public Key is exactly what is suggests - Public. It is made available to everyone via a publicly accessible repository or directory. The Private Key is also exactly what is suggests - Private, and must remain confidential to its respective owner. Because the key pair is mathematically related, whatever is encrypted with a Public Key may only be decrypted by its corresponding Private Key and vice versa.
For more information about PKI, please see http://en.wikipedia.org/wiki/Public-key_cryptography.