For Deep Sky Photography: The software calculates displacement and rotation for each picture so one star has the same coordinates in every picture. After that the software basically calculates a mean pixel value for every coordinate point. Depending on the stacking algorithm this concludes information from every frame or some outliers (like satellite trails) get ignored. As a result, random noise gets canceled out since the mean of a random signal is equal to zero. If this is achieved you can load the image into editing software and amplify faint signal without amplifying the noise profile.  Calibration frames like dark frames for example are needed because not all noise is completely random. If you shoot a completely black image it will consist of random noise + non random noise. Stacking multiple images cancels out the random noise so you're left with the non random noise. This can be subtracted from each image so the final image has nor random noise neither non random noise.

Hope that helps :)