I can't explain the schematic you posted. Can't figure it out. Doesn't mean it won't work just the same.
I think understanding will be easier if you examine the op amp Schmitt trigger. Also if you build one and experiment with it.
I've used hysteresis with an op amp. I got it to work but I can't remember how the feeback loop hooked up. The hysteresis concept is sort of an oddball
I do remember it took a lot of adjusting of resistor values, before I got it to switch states at my desired volt range.
Furthermore a proper explanation really needs two schematics. One showing node volt levels when the op amp output is high, and the other when it's low.
Then you can see in each case what volt level the signal has to cross, in order to cause a change of state.