Total Silence is a lightweight addon that helps you synchronize your interrupts with other players.
It automatically shares your interrupt cooldown with other players if they have the addon installed as well.
It uses three WeakAuras to display the information you need:
a) This icon shows you, that you should interrupt next. This icon is only shown to one player at any time, who has the highest priority.
b) It shows you how many players in your group/raid are using Total Silence (and have an interrupt) and how many of that have their interrupt not on cooldown right now.
c) It displays a timer which indicates that either the aura at a) will appear because your interrupt will go off its cooldown or the aura at a) will disappear because the interrupt of someone with higher priority will go off its cooldown.
The priority of each player is based on the cooldown of your interrupt with lower cooldown meaning higher priority. There are two exceptions which are demon hunters, who have a higher priority because they gain ressources from interrupts and restoration shaman, who have a lower priority because they are healers and should not worry that much about interrupts.