It is used for encapsulation of the SSL handshake protocol. The client authentication phase is optional. The asymmetric keys make it possible to communicate without a pre-established relationship. They are made up of a public key which is freely distributed, and a private key which never goes across the Internet. A public key and private key pair are mathematically related.
Cryptography is the mathematics of security.
Certificate Authority A certificate authority is a trusted third party. One could say the State of Florida is a CA, because it issues driver's licenses. A driver's license is a certificate because it says that the person matching the picture and the signature on the driver's license is indeed the name that appears on the driver's license. On the Internet, before a CA will issue a certificate it will run a background check. How thorough the background check is depends on what kind of certificate you want and are willing to pay for.