I think I've tried to explain this before. I'll try one more time, since many posters clearly don't get it, and keep making the same incorrect assertions year after dreary year.
Probabilistically, "significance" is entirely about perspective. This is true because probability is entirely about information, and information is dependent on perspective.
Many people incorrectly believe "prediction" determines significance. This is true, but only indirectly, because a prediction is either the result of or establishes a particular perspective.
Practically, this means two observers can witness the same event, and the event can be significant to one observer and insignificant to the other. Which, quite often, is exactly what happens.
Example: You're playing holdem poker. You have a lowly pocket pair of 3,3, which you played because no one raised and you have position. your only opponent in the hand is slow playing pocket J, J, hoping for some weak action. The flop is rainbow 10,9,5. Small, uninformative betting and calling ensues. Then the turn comes, a 3, giving you 3,3,3.
The turn 3 is very significant to you, giving you a hand that will be hard to beat, given the weak board and action by your opponent. But the 3 means almost nothing to your opponent, other than slightly improving his chances, from his perspective, because the 3 creates no obvious draws, is lower than his J,J, and a skilled opponent is less likely to play a hand containing or involving a 3.
You've both assessed the effect of the turn 3 correctly, given the information each of you have gleaned from your respective perspectives. But the turn 3 has provided much more information to you than to your opponent. Your perspective-determined information informs you that you probably have the winning hand. Your opponent thinks he likely has it, due to his relatively uninformative perspective.
Meanwhile, an objective observer who is not involved in the hand has no idea what any of the board cards imply. From his perspective, the board cards are just some random cards that came off the deck. He predicts to himself, based on his perspective, that whoever bets first on the river will take the pot. His prediction will probably fail. Your opponent will bet first on the river, but only has a 0.045 probability of taking he pot.
Meanwhile, it just so happens that the game is being televised, and the interested viewers know exactly what the facts are, thanks to the hole card cameras. They know your opponent has a a pair, and can beat you by catching a J on the river. That's actually not much more useful information than you have. The turn 3 was very informative to you. The only way you get disinformed and disemboweled is if a J comes on the river, a 0.045 probability.