What does a face-recognition system fundamentally do, in biometric terms?

It transforms a face into a digital signature and matches it against a reference database to verify or identify a person.

A face-recognition system is a biometric technology that detects human faces in digital images or video streams and compares them against a reference database. The standard pipeline is Capturing → Extracting → Comparing → Matching: capture the image, extract the unique facial features, compare against stored templates, and report a match.

It is primarily used for user authentication: it measures and analyses unique facial features to verify a person's identity. Put another way, face recognition "transforms biometric features into digital signatures that can identify people with high precision."

Tip: The "match against a reference database" step is the privacy-critical part — without a stored database of faces, recognition (as opposed to mere detection) is impossible.

Go deeper:

• Facial recognition system (Wikipedia) — the capture→extract→compare→match flow and identification-vs-verification.