It's a very, very bad misinterpretation of something that does have a legitimate scientific basis.
When the electrons around atoms are excited (i.e. absorb energy), they jump up to higher energy states, and then emit photons of light/electromagnetic radiation when they jump back down to a lower state. Since their states are quantized, the photons they emit always have certain specific amounts of energy, which correspond to different wavelengths of light -- the more energy, the shorter the wavelength (i.e. the higher the frequency). One of the main emission lines for neutral hydrogen atoms has a wavelength of 21.106 cm, which is in the microwave band (i.e. radio waves that are shorter than shortwave) and happens to be a wavelength that can pass through interstellar gas and dust easily as well as being able to penetrate the Earth's atmosphere. So it was the first wavelength that could be used for radioastronomy: using radio or microwaves to observe things about outer space that we couldn't detect with visible light. And since hydrogen is the most common (non-dark-matter) element in the universe, it let us discover a great deal about the shape of the galaxy and the universe beyond.
So that line about how "all matter in space vibrates in a specific radiation band" sounds like a case where the show's writers completely misunderstood what their science advisors were telling them. Yes, neutral hydrogen gives off radiation in that band, and most matter in space is hydrogen, but it's certainly not all matter, it's not the only wavelength it emits, and it's got nothing to do with vibration (that's confusing sound wavelengths with light wavelengths). I winced the first time I heard that line, and I've winced every time I've heard it since.