it spawns a new civ, called the Roman rebels and led by Pompey. they take a semi-random chunk of the empire along with the units there and declare war on Rome. if either side takes a certain number of cities or if peace breaks out all the cities flip back to Rome.
you can improve your relations with Rome by declaring war on the rebels, but I'd like to fix it so that if the Rebels are winning when the war ends then they take all their diplo factors with them when they take over. they could at least take their war/peace relationships with them.
ultimately if we aim for and achieve something reasonably historical Rome ends up more or less alone in the Mediterranean for quite a while so this is intended to provide some fluidity, a challenge for the Roman player and an opportunity for the other civs. for example if the east splits away even for a few turns, its a perfect opportunity for Pontus or the Greeks to grab the cities they need without declaring war on Rome. you even get a diplo bonus for declaring on the rebels.
edit: just had a funny idea. as the Roman player, assuming stability is such that you know you are going to have a civil war eventually (and I'd like it to be that way) you would naturally keep a stack at Rome and minimal garrisons elsewhere, not knowing which cities may split and wanting to give the rebels the smallest army possible. soooo... why not have the number of units in your capital affect the chance of civil war (ie make it more likely)... or maybe a smaller chance, based on the number of units in Rome, that Rome goes with the rebels... hmmm