The Rubicon was a stream separating Cisalpine Gaul from Italy. When Julius Caesar led his troops from Gaul to the Rubicon, Caesar paused on the northern end of a bridge debating whether to cross or not. It would be a crime against Rome for proconsul Caesar to bring his troops in from the province, but if he didn't, he would be stripped of command and prosecuted. Although he hesitated, Caesar did cross the Rubicon (although we are not sure exactly where), in January 49 B.C., thereby starting a civil war.
In "Caesar: civil war and dictatorship," Elizabeth Rawson says Caesar may have crossed the Rubicon on January 10, although the calendar was two months off.
To cross the Rubicon means to take an irrevocable step that commits one to a specific course. When Caesar was about to cross he quoted from a play by Menander to say "let the die be cast."
Source: Rawson, Elizabeth. "Caesar: civil war and dictatorship." The Last Age of the Roman Republic, 146–43 b.c.; Eds. J. A. Crook, Andrew Lintott and Elizabeth Rawson. Cambridge University Press, 1992.