Analogue tape can only hold so much signal. As the recording level rises it begins to saturate, adding harmonic distortion and rounding off peaks rather than clipping them harshly. Sound On Sound points out that tape’s character goes well beyond distortion: high-frequency sounds such as hi-hats distort at lower levels than bass, tape speed and head design create a low-frequency lift known as head bump, and wow, flutter and noise all play a part, varying with the machine, its alignment and the tape formulation.
That complexity explains why convincing tape emulation plug-ins model many variables at once. In jazz lo-fi, tape saturation, real or simulated, is used to soften digital edges, tame transients and give a recording the comfortable feel of a cassette or reel-to-reel copy.