When the alarm sounds, the specified action will be executed if the alarms are not blocked and the alarm and the alarm group it's in are turned on.
Note that if you reset your system clock, the program will take at most around 30 seconds to notice the change. All alarms which were 'missed' if the clock was set forward will sound at most 30 seconds later.
If you chose to display the message window as an alarm action, you can set the alarm to snooze for a specified amount of time. You can choose to add this time to the time the alarm sounded (or was supposed to sound) or to the current time. The alarm will sound again after the specified period has passed.
Note that when an alarm has sounded after a period of snoozing, it is not shown in the list with past alarms. It however will be shown in the list of coming alarms when it's still to sound.
Also note that if a periodical alarm sounds and you let it snooze for a longer period of time than the period length (so that the same alarm will sound again before the snoozing is done), you'll be asked if you want to override the snoozing if you set a new snoozing period.