Maybe an example could help explain it; a customer runs a multistory carpark with 20 levels with the fire panel being in the control room on the ground floor. A detector goes off on the 19th floor in a plant room which is locked and out the way. The panel is programmed NOT to sound any audible output until 1 minute has passed.. The security staff are on their way to the area thats in alarm, but 45 seconds has already passed and they are only on the 15th floor.. The operator in the control room after getting an update from the guard, then presses the VERIFY button which gives the guards another 60seconds to find the device in alarm. (ie. the alarms wont sound before that extra minute has passed)
If they get there and find there is no fire, pressing the silence button will cancel the time delay and silence the system (ie. the alarms wont sound however much time passes).... If there is a fire, they could either let the panel sound itself by letting the delay time-out or if they have only just pressed the verify button again, pressing evacuate would sound the alarms.
Hope that is of use, and I havent waffled on too much.