Symmetric and asymmetric ciphers each have their own advantages and disadvantages. Symmetric ciphers are significantly faster (Schneier states “at least 1000 times faster”) than asymmetric ciphers, but require all parties to somehow share a secret (the key). The asymmetric algorithms allow public key infrastructures and key exchange systems, but at the cost of speed.
A hybrid cryptosystem is a protocol using multiple ciphers of different types together, each to it’s best advantage. One common approach is to generate a random secret key for a symmetric cipher, and then encrypt this key via an asymmentric cipher using the recipient’s public key. The message itself is then encrypted using the symmetric cipher and the secret key. Both the encrypted secret key and the encrypted message are then sent to the recipient.
The recipient decrypts the secret key first, using his/her own private key, and then uses that key to decrypt the message. This is basically the approach used in PGP.