With Q4 turned off, R7 turns on Q5 and the output is driven low. R7 + R8 currents flow through R9, dropping almost 200mV.
With Q4 turned on, Q4 saturates and turns off Q5. Only R7 current flows through R9, dropping less than 100mV.
Reminder: bipolar transistor behaves very much like a diode, in that its current increases sharply when base-emitter voltage crosses some 0.6~0.7V, depending on transistor type, temperature and magnitude of current being switched.
Hence Q4 switches when its base is about 650mV above R9 voltage.
The low to high threshold is 200mV + 650mV or 0.85V.
The high to low threshold is 100mV + 650mV or 0.75V.
This explains the hysteresis.
During transition, R9 voltage begins to change in the direction which accelerates the transition.
This gives the fast output edges.