The Radiometer Equation relates bandwidth, length of observation, and amount of random noise, to a resulting Signal-To-Noise Ratio (SNR), i.e., your ability to tell whether a Radio signal is coming from a specific direction. It is of interest in any situation where the sensing ability of a radio receiver is of interest, including Radar and communications as well as Radio Astronomy.
There is random noise from the sky, from the antenna, and from the circuits and transmission lines themselves. An assurance of the presence of a signal of interest can be derived if the observation time is sufficiently long. The gist of the equation is to characterize to what degree random noise might masquerade or cancel a signal according to the above factors.
Radio observations also pick up competing (non-random) signals because no antenna is perfectly directional. These are generally accounted for by noting the characteristics of the antenna's directionality and by observing in other directions, generally near the direction of interest. This is somewhat analogous to Apodization for Optical telescopes.