How is reflectivity measured radar?

A radar signal is an electromagnetic (EM) wave, and as such will travel at the speed of light in the atmosphere. If part of the space has different EM properties, then some of the wave will be reflected from that region.
Solid objects are the most conspicuous, but rain radar sees the changes in the atmosphere caused by the rain clouds.

One of the most remarkable uses for radar is to measure the wind profile behind an aircraft carrier - the place where the incoming planes approach their carrier.
For this, a very brief high energy acoustic pulse is sent out, and this will cause compressions and rarefactions in the air behind the carrier.
Amazingly (to me) these minute differences in the EM properties of this space can be picked up by a radar.

The carrier always steams into the wind (when active) and the wind flows along the deck, and drops down in the wind shadow behind the carrier. This is precisely where the incoming plane is aiming to land, and a 'down draft' at this point will not help his accuracy. Thus the knowledge of the wind profile is of great value to the flight controller and the incoming pilot.