Rome developed as a Republic with unusually expansive voting rights. It was led by co-consuls who alternated days they were in power. The Senate was a powerful body indeed and with this system, the interests of the Plebeians (the poor, common folk) actually had occasional bouts of good will where the Patricians (the wealthy who controlled things) took care of some of their desires.
It was the Senate that decided whether or not military leaders would be granted a Triumph. Triumphs were parades to celebrate some notable military accomplishment and the glory for receiving one was the goal of virtually every General.
However, it was just the general who received it. Armies were not allowed near Rome. To bring an army inside the barrier of the Rubicon was a violation of all the Roman Republic held dear and brought the weight of the entire Roman nation against the offender.
Only someone who was supremely confident (read "arrogant") would dare to bring an army across the river. Enter Julius Caesar. He had a long and interesting career that careened wildly from success to defeat. Working with and opposed by some of the greatest names in Roman history, he went from great military conquests to the consulship, back to the military and so forth.
To his credit, he did try to take care of his soldiers and to some extent of the poor of the land. But he had a rather self-centered outlook on things as well.
As an example, early in his career he was captured by pirates who, while he was in captivity, he promised to crucify. After his ransom he raised units sufficient to capture the pirates. His superior ordered him to sell them into slavery but he instead crucified them under his own authority...an egregious exceeding of his authority and rights that went unpunished.
Julius would grow used to exceeding his authority and getting away with it which is perhaps what led to the events of January 10, 49 B.C.
Returning from a consulship, he paused at the brink of the Rubicon. Already he had rebelled against the decree of the Senate in bringing the troops with him. However, he could easily overcome the consequences of this minor disobedience by turning back.
Instead, he crossed the Rubicon with his soldiers. There are different ways of saying what he said...Plutarch claims he said, "Let the die be thrown" but I prefer the more poetic Suetonius who claims he said, "The die is cast".
Either way, the truth is the future had changed direction. The crossing of the Rubicon was a fundamental shift in the outlook of the Roman nation. Shortly Caesar would win the Civil War when he defeated Pompey, the only real opposition.
After this, the nature of Roman politics changed. At first it was Julius being voted "dictator" for a year a couple of times, then for a ten-year period (during which he was assassinated).
Prior to this, Dictator was granted only in times of tremendous military distress and was only for the duration of the conflict. It was considered a duty rather than an honor and had none of the negative connotations we associate it with today. That began to change with Julius.
Setting aside the good and bad things he did, it is important to note that henceforth the Roman political system we are more familiar with of one King-like figure, generally called the Caesar, replaced the much more inclusive consuls and Senate system. And all because he crossed the Rubicon.
Thus we have a phrase that, at its smallest level, means to take a step that has serious consequences and cannot be turned back from, but at its greatest level can call to mind one of the pivotal moments in history.