In my presentation on the Stanford Dish, I mentioned that the Dish was originally created to monitor the Tall King Soviet radars. I decided to read through the declassified paper (found here) to understand better how it works, and here is what I have gotten from the paper.
The military wanted to know the position of the Tall King Soviet radars and the parameters they were operating under. Such information can be extracted from the signals transmitted by the radars. However, such signals were seldom detected because the wavelengths of the signals were too short for them to be deflected by the ionosphere. Therefore, most of the signals would be lost to outer space. Also, flying a plane into Soviet territory to gather information was feasible, firstly because that was prohibited, and secondly because a airplane would be unable all the sophisticated machinery required, and they were pretty heavy.
The scientists were unsure what could be done, when they suddenly detected in 1946 man-made signals coming from the moon. After many experiments, known as the Moon Bounce tests, they were able to prove that these signals were reflected signals, and they could extract reliable information out of them. This provided some hope.
However, there were still some challenges that needed to be overcome. For example, whether signals from the Tall King Radars would be reflected by the moon and detected by the receivers in the US is highly dependent of the time, the location of moon and the location of the receiver. After some consideration, it was decided that California was one of the better locations to build a Dish, and that was how the Stanford Dish was created.
For more information, check out the paper!