One problem with comparators is that the signal is often noisy, and when the input voltage is close to the threshold voltage, a little bit of noise can make the voltage vary to levels that rapidly fluctuate to values just above or just below the threshold voltage. This can cause output "glitches", that can make control systems unstable.

The following is a simple comparator circuit with...

V1 =10V Peak-to-Peak signal
Noise= 1V 2.5K Hz singnal

V2 = 3V




The output is the following in green...
You can see that when the comparator gets near the 3V signal the output of the comparator will have glitches.


You can solve the problem by adding hysteresis to the circuit.
This can be done by adding a feadback resistor as show below.




Now running the simulator agian... we get...



A system employing hysteresis depends on the current state/output of the system, a system with hysteresis has "memory"..
That is, it's reponse depends on the past. Some people remember this by associating "hysteresis" with the word "history".