When a beam strikes a raindrop, or hailstone, part of the beam will be reflected back to the radar. The radar receives the reflected beam, and can calculate the precipitation's distance away, as well as its intensity (based on size and speed of drop), and which direction it's moving, if it's windy.
The radar will then translate the distances and intensities into a graphical map that we can display on TV. The radar we use is sensitive enough to track wind blown particles, and even bird migration patterns! However, we set a filter to keep those off the weather maps.