Diode on op-amp output to drive tube
It's a form of deliberate distortion, which is popular in some guitar styles.

If you look at your blue simulation waveform, you can decompose it into two components:


the original sinewave (about 3.4 Vpp)
a square wave (about 0.8 Vpp) at the same frequency that has the same zero crossings.


This adds a series of odd harmonics to the signal, which gives it extra "buzz" or presence.

This is not the same as a clipping circuit, which only kicks in at high input signal levels. This effect applies at all signal levels. In fact, this effect is MORE pronounced at low signal levels.