Triggers can be turned off -> even when the event is carried out, if the trigger is turned off, it won't fire no matter what.
Initially On means it's turned on. If you uncheck the box, you will turn it off.
Example:
If you create a trigger which fires every 5 seconds and writes some message, you will see that with Initially On it will show the message in game, while when it is uncheck, it will not show the message even once.