Why was it important that Caesar crossed the rubicon?

The Rubicon was/is a river in Northern Italy.

The thing that made it important in this specific case was that at the time it marked the boundary between Gaul, a province in the Roman Empire (where Gaius Julius Caesar had the legitimate legal authority to command troops) and Italy proper, controlled directly by Rome, where he did not. The Latin Word for this right of command was imperium.

It was a capital (death) offense for anyone but a consul or praetor (elected officials) to exercise imperium in Italy. It was likewise a capital offense for a soldier to obey such orders. Generals were supposed to formally disband their armies before entering the home territory.

When Caesar crossed the Rubicon with his army intact, he was effectively declaring civil war. Had he not won, he (and his army) would have been executed. Up until the moment they crossed the river, they could have turned back, as they had not up until then violated Roman law.