Way back in the day, a man named James Clerk Maxwell said that math is the glue that unites electricity and magnetism. And that's about it. That's how it got here.

…You didn't believe us, did you? Good.

Maxwell's theory of electromagnetics believed that the speed of electromagnetic energy is just like the speed of light. (He was a little backwards, seeing as light is a form of electromagnetic energy, but we'll let it slide because his theory was so on point.)

Maxwell also predicted that the frequency of the electromagnetic wave would play a large role in figuring out whether his theories are true. Heinrich Hertz, a big fan of Maxwell, figured out a way to use Maxwell's equations to make a device that tested frequency by making radio waves. These waves are longer in wavelength and lower in frequency than visible light, which was the key to figuring out this spectrum. (Source)

These experiments in the late 1800s showed that

1. radio waves exist.
2. they can pass through things like clouds or water. 
3. they're reflected by metal.

That metal piece is kind-of a big deal, since we already knew that mirrors (which are made from glass on top of metal) reflected visible light. The fact that it worked for radio waves, too, drew another connection to light.

Before radar could be invented, Christian Hülsmeyer had to invent the telemobiloscope in the early 1900s.We're telling you this partially because telemobiloscope is such a cool name (seriously: A+ on the name, Hülsmeyer) and also because it uses the properties of radio waves to detect metallic objects. It was meant to be an early warning system for ships to locate other, metallic ships in bad weather like fog.

(If only icebergs were made of metal; his device could've saved Jack's life.)

Now that we had the device to send radio waves, we needed a way to use them to measure distances. That's where Edward Victor Appleton comes into play. Appleton discovered that when he pointed radio waves at the sky, he got multiple reflections back. Not only that, but he also found that the time delays of these reflections were different at night than during the day. He was so intrigued about the multiple reflections and the changing time delays that he worked out a geometric way to find objects that produce radio wave reflections.

It took another two decades, lots of war funding (hello, World War I), and lots of scientists working in secret to develop the modern radar that both detected and located a reflecting object. The scientist who put all that science together to create a radio detecting and ranging system was Robert Watson Watt. (Source)

Watt figured out everything from the oscilloscope that makes the radio waves to the formulas that found how far away an airplane is. He worked tirelessly to develop the modern radar in 1935 but it was the American military that came up with the catchy acronym RAdio Detection And Ranging system. As far as acronyms go, that's a pretty great one. It's right up there with

• LOL
• TED
• EVIL