Android - Whats the use case of proximity sensor?

The proximity sensor on most smart-phones with touchscreen exists to disable accidental touch events. The most common scenario is the ear coming in contact with the screen and generating touch events, while on a call.

mobile phones use IR-based proximity sensors to detect the presence of a human ear. This sensing is done for two purposes: Reduce display power consumption by turning off the LCD backlight and to disable the touch screen to avoid inadvertent touches by the cheek. IR sensors have a number of disadvantages, including high power consumption, high cost, blind zones, and accumulation of dirt, as well as unreliable performance over temperature, hair, and skin color variations.

It prevents that your ear is doing input actions on the touchscreen when you are making a call. :)

Most proximity sensors are simply light sensors that will detect "proximity" when they are covered.