Or, putting it in these terms: Say you had a (signal) that activated a relay. You might want to add hysteresis so the relay didn't chatter.
Or
Say you had a controller like your UPS that needs to make 120 VAC. 120 exactly might cause problems, but making it 120-124 V makes the system more stable.
Filling a tub is a large amount of hysteresis. You would have an empty switch, a full switch and say a 1/2 full switch.
When the tub is emptied below 1/2 if fills to full. Your saving wear and tear on the pump. the pump might have to constantly start and stop.
Just some examples.