These are generally called supplemental lenses. They mount in front of the phone’s built-in lens and change the way light enters it, much like eyeglasses change the way your eye focuses.

They work the same way supplemental lenses have long worked on regular cameras:

• A close-up/magnifying attachment can let the camera focus much nearer for macro-style shots.
• A telephoto-style attachment increases apparent magnification.
• A wide-angle attachment spreads the field of view to capture more of the scene.

The phone camera still does the actual image capture; the add-on lens simply modifies the optical behavior of the existing lens. This is not unique to smartphones—similar front-mounted accessory lenses have been used on cameras for many decades.