The basic concept of hysteresis is that if you just had a single "switch temp" you would get nothing but short cycling as you would hit the temp and trigger the pump or whatever, which would shift you away from the temp and turn you off, etc...
Say you had a thermostat on the water jacket that had a single switch point of 150* to turn on a circulator pump - the boiler fires, hits the switch point, and the pump turns on - soon as the cold return water enters the boiler the temp drops, and the thermostat would turn the pump back off, so you'd end up with the pump turning on and off every few seconds, and very little actual water circulation.
Instead they separate the "turn on" and "turn off" points so that you get a reasonable cycle time. In the example above, they might still set the temp where the pump turns ON at 150*, but not allow it to turn off until the water temp drops to 130* - as long as the boiler can heat the water enough to get it above that temperature, the pump stays running, so your cycle time is reasonably long.
On your house thermostat, you will typically see a 3-4 degree hysteresis spread, which is the same thing - you set the thermostat to 65*, the heat might not come on until you drop to 63*, but then will stay on until you hit 67* for instance. (and if you poke around the thermostat, you will usually find an adjustment for this amount of spread)
Fairly typically you will have a setting temperature, and then a control for how much separation you get between the two temperatures, or the "differential"
It takes a bit of care to make sure the spread is going in the right direction, but usually the control will take care of that if you are using it in the way it was intended.
The setting is essentially a compromise, and you have to decide what factors are most important - in general the wider the spread, the longer the cycle, which is good, but you may run into comfort issues, or getting above or below a safe operating parameter... The narrower the spread, the more precisely you will maintain the setpoint value, but the shorter your cycle time, which can cause inefficiencies or other problems. In each case you have to decide (or follow the manufacturers reccomended decision) about how much differential is going to give you the best performance.
For instance, if you have an excessive spread on your house thermostat, you will find comfort problems as you cycle between too cold and too hot. If the spread isn't wide enough, your heating system will short cycle excessively....
Gooserider