Tape saturation
The soft distortion magnetic tape produces when fed more signal than it can take — a technical limitation that became a sought-after sound.
Tape can only be magnetised so far. As the level approaches the ceiling the transfer curve bends over gradually instead of hitting a hard stop, so peaks get squashed and odd harmonics, mostly the third, are added. The effect resembles a slow compressor with a dash of distortion. Engineers learned to "hit the tape" deliberately on drums and bass, where it sounded denser and warmer.
Digital recording has no such ceiling, just a wall at 0 dBFS where clipping sounds ugly. Hence the crowded market for tape-emulation plug-ins, which also mimic wow and flutter, hiss and the low-end lift known as head bump. Good ones oversample, because otherwise the added harmonics fold back down as aliasing.