Breach day is term used by CLEA in relation to the date that Rift first used his abilities to visit another reality. Up until this date he had only visited the void between realities and had no idea that he could reach another “Earth”.
In trying to save a civilian aircraft he over extended his abilities and ended up sending himself and the aircraft to another reality. After working out what had happened it took months for him to find a way to bring himself and the displaced survivors back to our reality.
The event is significant to CLEA since when Rift managed to create a passageway to another reality he simultaneously opened breaches around the globe to other realities which saw and influx of people form alternative versions of Earth. Whilst most of these were created by chance due to Rift not having realised what he was doing there are many theorists who think our reality was very secure and there were people waiting to come to our reality. All that was needed was a weakening in the barrier that separated our reality from the others.
An example of this might include the Emerald Dragon who was imprisoned by evil forces in another reality and was finally able to escape on Breach Day.
Since Rift is now aware of his full potential and has taken steps to prevent the creation of random breaches, CLEA doubts there will be another repeat of the event any time soon.