The expression means that an important decision has been taken and there's no way of turning back

The die is cast, our decision is made and we cannot turn back

Ormai il dado è tratto, la decisione è presa e non possiamo più tornare indietro

When the opposition senator returned to the Senate chamber from a long illness in order to vote against the bill, he needed no more than a glance to see that the cause was hopeless. "If there is anything I could do," he said, "I would do it. But I assume the die is cast."

Quando il senatore dell'opposizione rientrò in parlamento dopo una lunga malattia per votare contro una mozione, si rese conto immediatamente che era una battaglia già persa e disse: "Se ci fosse qualcosa che posso fare, la farei; ma ho paura che ormai il dado sia tratto e i giochi siano fatti"

Translation from the Latin "Alea iacta est", phrase uttered by Julius Caesar on January 10th, 49 B.C., before leading his army across the Rubicon river in defiance of the Roman Senate. The Rubicon, in northern Italy, marked the boundary between the Cisalpine Gaul and Italy; by crossing it, Caesar entered Italy at the head of his army without the Roman Senate consent, became an enemy of Rome and set the long civil war against Pompey and the Optimates in motion.