how is the microwave sensor work？

A microwave sensor is an electronic device that detects motion, and can be used to control luminaires. Microwaves operate differently to PIR sensors, by projecting microwaves, which bounce off surfaces and return to a sensor within the detector. By analysing this information the sensor can detect any movements within its range and do all this in less than a microsecond.

and what are the benefits?

Generally, microwave sensors have much better sensibility compared to the PIR sensors.
Microwave sensors can also perform well if there is any metalloid barrier, which the PIR sensors cannot.Microwave detectors can be used in virtually any environment, including those that are not otherwise hospitable to sensors, such as high heat environments that can set of photo-electric sensors. This makes them one of the most versatile types of sensor system.
Microwave detectors can go through walls and holes. Because of this they can cover a larger area of a home or commercial property, including fairly large outdoor areas. Microwave sensors that are more advanced can also detect whether an individual is moving towards or away from the sensor, or moving randomly. There are ways that some trained individuals could potentially move to avoid detection by a motion sensor.