Without going too far down the audio theory ‘rabbit hole’, volume level is measured in decibels (dB). They applied many clever techniques for getting rid of the “noise floor”, the name given to the volume at which the unwanted background noise sits.
The two most prominent figures of this industry were - arguably - Dolby and dbx. Since magnetic tape was used all the way through the professional recording process, a whole industry spawned out of technologies dedicated to reducing that hissing noise. On the more expensive tapes you could buy - such as chrome (chromium dioxide) or metal (purer and non-oxidised) - the particles would be smaller, and that meant less hiss on playback, as well as better dynamic range and frequency response. The hiss you heard was caused by the size and type of the magnetic particles used to make up the surface of the tape. The problem with recording onto tape was that, when played back, in the background you would hear a lovely, hissing sound.
In fact, back in the days of the good ol’ cassette tape, noise reduction techniques were paramount. Noise reduction techniques have been around for many years, well before the advent of digital audio. Ahh, the humble Boots cassette tape, juxtaposed against a background of classic iPods.