The play is set around 491 B.C.E., when Rome is in the early stages of being a Republic. King Tarquin has just been overthrown and replaced by a government run by elected officials.
Rome may be well on its way to setting the precedent for modern democracy, but it's still a violent, war-torn place where two different social classes are struggling for power. In other words, it's a hot mess—and that makes it the perfect backdrop for Shakespeare's final tragedy.
See, historians have pointed out that this conflict seems to dramatize some 17th century political issues. When Shakespeare wrote Coriolanus, King James I was doing his best to rule England as an absolutist monarch (a king who does whatever he wants and doesn't have to answer to anyone else.) The English parliament was all "Not so fast, King James," questioning his rule and demanding a lot more say in how the country was being run.
Coriolanus also may echo some hot-button social and economic drama that Shakespeare would have known about. The opening riot seems like a good bet for a shout-out to the infamous Corn Riots of 1607, which went down in the English Midlands around the time Shakespeare wrote Coriolanus. Why all the rioting? Well, England experienced a series of food shortages in the late 1500's and early 1600's because a bunch of common land was enclosed for grazing rich people's cattle instead of planting poor people's crops. In other words, the poor and the powerless got screwed over big time...and they didn't exactly keep quiet about it. Sound familiar?