It shoots three orthogonal laser beams out the cabin window. Some of the laser light bounces off dust particles, and is reflected back to the device. It is able to measure the aircraft velocity on each of the three orthogonal axes, and thus determine the true airspeed, angle of attack and angle of sideslip. They combine the TAS with static pressure from the static ports and outside air temperature and then calculate calibrated airspeed.
Laser anemometers can become unusable in very clean air (such as high at high altitude) due to the lack of particulate matter to scatter off. Having said that, water droplets in clouds would do nicely. And the fact that such a device can operate from behind glass could remove the problems of icing faced by a pitot or ultrasonic (or direct pressure) solution.
The appeal of the time proven pitot static method is that it is a direct physical measurement of the very dynamic forces that are keeping the aircraft flying. If the only real problem is icing, then that suggests simple redesign rather than technology replacement.