A hydrogen atom is composed of a proton and an electron. Both these particles have a spin degree of freedom. Spin is a purely quantum mechanical concept, but there is some analogy with a bar magnet. So in a hydrogen atom, the spins of proton and electron can either be aligned or anti-aligned. In the bar-magnet analogy: either the north-poles of both magnets point in the same direction (aligned) or in the opposite direction (anti-aligned).4.5 And just as in the bar-magnet case, there is a small energy difference between the two states, with the aligned state having higher energy. Transitions between states of different spins are also called hyper-fine interactions.4.6
When an HI atom with aligned spins is left on its own, it has some small probability for a spontaneous spin reversal to the lower energy state. When it does so, it emits a photon with wavelength 21-cm. The mean time it takes an HI to perform such a spin reversal is several million years. This makes it almost impossible to observe this transition in the laboratory, because collisions between the particles will de-excite the aligned spin well before there has been a spontaneous transition. But in the ISM, densities are far lower than can be generated in the lab. The 21-cm line is of great observational value. First of all, there is enough HI to observe the line. And once the line is produced, its low probability becomes an advantage, since the 21-cm radiation can pass through a lot of HI gas, without it being absorbed again. Given the long wavelength, 21-cm radiation is not absorbed by dust.
An external magnetic field shifts the energy levels (called the Zeeman effect). And so 21-cm radiation can be used to estimate the strength of the magnetic field in the ISM.
It was the Dutch astronomer Jan Oort who suggested one of his students, van der Hulst, to compute the wavelength expected for this transition. (Wouldn't you like to be given such a project?). When it was clear that it could be observed, he asked the government for money to build a radio-telescope to go an observe it.