While difficult to define in an all-encompassing manner, probably one of the best definitions of biometrics is:

The use of physiological or behavioral characteristics of a human person through automated technological means to determine or verify the identity of that person.

Physiological biometrics use algorithms and other methods to define identity in terms of data gathered from direct measurement of the human body. Finger print and finger scan, hand geometry, Iris and retina scanning and facial geometry are all examples of physiological biometrics.

Behavioral biometrics are, however, defined by analyzing a specific action of a person. How a person talks, signs their name or types on a keyboard is a method of determining his identity when analyzed correctly.

Biometrics can furthermore also be defined as either Passive, or Active. Passive biometrics do not require a users active participation and can be successful without a person even knowing that they have been analyzed. Active biometrics however, do require a person cooperation and will not work if they deny their participation in the process.

Active Biometrics:

All Fingerprint technologies
Hand geometry technologies
Retina scanning technologies
Signature recognition technologies

Passive Biometrics:

Voice recognition technologies (limited)
Iris recognition technologies (limited)
Facial recognition (truly passive)