When using a biometric application for the first time the subject needs to enroll to the system.
The system requests the biometric factor (fingerprints, voice recording, etc.) from the subject, this input is registered in the database as a template which is linked internally to a subject ID. The next time when the subject wants to authenticate or identify himself, the biometric input is compared to the template(s) in the database by a matching algorithm which responds with acceptance (match) or rejection (no match).
In most cases not the raw data of the recording (e.g. image of the fingerprint or iris) is stored, but a digital representation generated by an algorithm, a good example of this is IrisCode.