Authentication is the process by which a user establishes his identity to a system or application. Users authenticate using authentication factors which may broadly be something the user is (biometric), knows (secret) or has (a device).
Multi-factor authentication is authentication with multiple authentication factors (alternately referred to as credentials). The idea is to increase the reliability of the authentication process -- making it harder for an attacker to fool -- by combining the strength of multiple techniques.
Examples of multi-factor authentication include: