Basic Understandings

Radar, short for RAdio Detection And Ranging, transmits microwaves as a focused signal designed to detect precipitation-sized particles in the atmosphere (rain, snow, hail, etc.)
Radar energy travels in a narrow beam through the atmosphere at the speed of light. The radar antenna directs the beam around the horizon and up and down at various angles until most of the sky (within a given radius around the radar) has been scanned.
After a radar sends out a signal, it "listens" for a return signal, or echo. An echo occurs when the signal reflects from objects (e.g., raindrops, ice, snow, trees, buildings, etc.) along its path.
Part of the reflected signal is received by the radar antenna. The display of the strength of echoes is called reflectivity. Reflectivity can be correlated to the intensity of precipitation.
The direction the antenna is aimed determines the direction to the target; the time from transmission of a signal to the reception of an echo determines the distance to a target.
Modern weather radars can also evaluate the returned signal to detect target motion toward or away from the radar using the Doppler effect.