In the (time shortly after the) beginning the universe was formless and void, and all that existed was hydrogen and hydrogen was all that existed. Over time the hydrogen clumped together through various forces such as gravity. Eventually enough hydrogen clumped together that the force of gravity was sufficient to trigger nuclear fusion. And then there was light.
Hydrogen can absorb or (suitably excited) emit light at 21cm wavelength specifically, better than all other wavelengths. So from the background smorgasbord of frequencies emitted by the extremely hot hydrogen of the first stars (“First Light”) the cold hydrogen would have absorbed some as heat, and absorbed more at 21cm as excitation energy.
So assuming a relatively linear distribution of wavelengths in First Light (you could call it “white” light) there will be a portion where photons at 21cm were absorbed by hydrogen.
So the Cosmic Dawn signal is distinct because of what it is missing.
Based on the article, I don't think this is right. http://astronomy.swin.edu.au/cosmos/S/Spin-flip+Transition, linked, describes the 21cm emission as occurring once every 10 million years for a single atom.