Resettable latching switches
The function you're looking for is very common in, for example, a sump-pump controller. If the sump starts to overflow (because the pump has failed), an alarm contact closes, and it usually sounds a very loud buzzer. There's a momentary-action switch called "Alarm Silence" that will shut off the buzzer (so that you can fix the problem in peace), but then it will re-arm itself once the original alarm contact opens.

It is easily implemented with a single SPDT relay, as shown below. S1 is the alarm contact, S2 is the "silence" pushbutton, and the relay K1 keeps the load (buzzer) switched off until S1 opens again and the relay drops out. "Power Source" and "Load" can be pretty much anything, as long as the coil of K1 is compatible with the power source.