Roman politics were a confusing, brutal, and byzantine (heh) mess. I'll provide a few quick pointers for those of you not in the know or just a little rusty on your 2000-year-old political intricacies.
First off, the core of Roman politics in the late Republic: the Roman Senate, and it's divisions, the populares and the optimates.
The Roman Senate was the core of the Republic. Headed by two consuls who were elected every year, the Senate was composed of land-owning nobilis, Romans descended from Romans who had already sat on the Senate, or who had earned inclusion into the Senate through bravery or prestige. The populares and optimates were largely unofficial factions in the Roman Senate, organized along political lines.
The populares, as the name implies, were of the people. They courted the plebians and the lower classes, promising to fix their problems, inequalities of wealth, and provide them with jobs, food, and security -- the same things the poor have always wanted. The populares was often the party of demagogues and rabble-rousers, senators who rose to power by giving long speeches about making Rome great again. It was notably also the party of soldiers such as Gaius Marius, Mark Antony, and Julius Caesar, all of whom won glory on the battlefield and harnessed it into popular support at home. The populares were defined by their willingness to appeal to the people and use their popular support to defy the traditions and rules of the Republic, ultimately circumventing the democratic ideal of Rome.
As the game starts, the populares are the party of Gaius Marius, Rome's most famous general, who, with popular support, has seized the city of Rome from his enemy Sulla and the rival optimates.
The optimates were the polar opposite of the populares. Anchored in four centuries of tradition, they were the party of the aristocracy and the patricians, devoted to reducing the power of the plebians and the common folk and increasing the power of the Senate itself. By their nature conservative, they sought to keep the status quo of the Republic and prevent opportunistic generals like Caesar from becoming dictators.
Now, however, they are the party of Lucius Cornelius Sulla, a general almost as famed as Marius, who opposes the progressive reforms of Marius and his populares. Overseas defeating a rebellion in Greece when Marius seized power, Sulla is returning to Rome with a legion at his back as the game begins, and is supported by many old and powerful noble families in Rome herself.
These were not hard parties as we think of them today, but rather described the way a Senator chose to act. A Senator could, at different times through his life, court the people and support hardline legislation that curbed their rights. The populares and optimates were used to group senators who, at that moment in time, chose to consistently appeal to either the people or the aristocracy for support. They did not always work together as a unified party, and some often switched allegiances as convenient.
Now, one wonders, how can this be a democracy if the aristocrats control everything?
Well, to put it simply, they don't.
The People's Assembly, composed of all the plebians, or common people, of Rome, elects a Plebian Tribune each year. These tribunes represent the common people to the largely patrician Senate, and can convene the Senate, propose legislation, and act for the people in legal matters. Their most important power, however, is the veto, which gives the people a measure of control over the largely patrician Senate. Any assault on the person of a tribune is against the law -- a fact many tribunes have used to their advantage to physically stop the Senate from voting on a bill.
The plebs, optimates, and populares will all come into conflict in the waning years of the Republic, and Roman politics still hide a ocean's worth of complexity and mazelike contradictions, but this starter should get you brushed up on the terms that will be used frequently in this Quest.