As soon as the condition becomes true, it will trigger once. So, for example if you have an event such as "Keyboard - Space is down," then as soon as the key space is pressed down it will trigger the trigger once event which will, hence the name, trigger the actions once.
Here is an example. So, if we did not have the trigger once event, every tick the player overlapped the coin, the sound would begin to play. Obviously we do not want that so we put the trigger once event. Although in this case there is an easier way to do this without trigger once which is to just use the "on collision" event.