Radio waves are the lowest frequency waves on the electromagnetic spectrum. They are made of electromagnetic energy, moving in a wave pattern, that can pass through both a medium (like air) and also through a vacuum. The frequency and the wavelength determine what "kind" of wave you get - radio, light, x-ray, etc. They all travel at light speed, and all can be reflected or refracted the way light can.
There are many examples of why radio waves are significant. Because they can cross space, they are used extensively by astronomers. Most stars emit radio waves, and by studying these we can learn about the structure and history of the universe; some of the largest telescopes in the world don't use light at all, they are so-called radio telescopes.
Radio waves are also used for communications. In addition to commercial radio broadcasts, radio waves operate short-wave and citizen's band radios, walkie-talkies, and cell phones. Microwave ovens use specific wavelengths of radio waves to heat food.
The other significance is that large doses of radio waves are known to be harmful to the human body, essentially the equivalent of sticking your head in the micorwave. This is why so many studies are being done to determine whether cell phones cause cancer or not. The jury is still out on that at the moment, but scientists are urging people to be careful, just as a precaution.