Kerberos is a network authentication system based on shared key cryptography. It uses a central service called a KDC, which answers authentication requests from clients and allows for a lot of central control (such as centrally locking users). It is the authentication protocol underlying Active Directory and is widely used by large organizations.
One nice property of Kerberos is that, when fully implemented by all protocols used by the user, the user's credentials (password or key) never leave their local system. The only thing that leaves the system are authenticators with a relatively short lifetime, which greatly reduces the risk when other systems are compromised. However, it is common to have to occasionally send Kerberos passwords to a server for validation over SSL, which diminishes this benefit.
Kerberos is commonly used via GSS-API (Generic Security Service API), often via a protocol framework such as SASL or SPNEGO.