This lets you speak a name to dial a number instead of entering a number manually or choosing it from the phone book.
There are two types: speaker-dependent (recorded) and speaker-independent (recognition).
With speaker-independent voice recognition, no recording/training is required. The name can be spoken by anyone, and the phone will automatically understand the spoken name and match it with the closest name entered in the phone book. On smartphones, speaker-independent voice dialing is just one function of a comprehensive voice assistant feature that recognizes and "understands" a wide range of voice commands.
With speaker-dependent, voice dial entries (or "tags") must be explicitly created by speaking and recording the name 1-3 times. The phone will only respond to recorded names, and usually only when spoken by the same person who recorded them. This uses a very crude audio-matching technology instead of actual voice recognition. The maximum number of voice dial entries is usually limited to a fraction of the size of the whole phone book.
Speaker-independent is the most common type, available on all smartphones. If the type isn't specified, it is usually speaker-independent. Some very old phones (not smartphones) offered only speaker-dependent voice dialing.