The canon history of Firefly and its universe revolves around the idea that Earth became grossly overpopulated, using up all natural resources and forcing humankind to relocate among the stars. The history before this, generally referred to as the “Earth-that-was”, is essentially our world and our history. Given this premise, the events that followed leading up to the time the story took place is presumed to be nothing more than history repeating itself on a new level of experience.
Approximately the time when the Earth’s resources were being exploited by war and overpopulation, the Alliance was formed between the United States and China, ultimately a possible next step in globalization. This effectively merged the two cultures as Earth became uninhabitable, and multigenerational spaceships were sent out to colonize another planetary system. The planets were colonized and governed by the Alliance, much in a manner similar to that of the colonization of America after the population began traveling from Europe to seek a new start.
Eventually, like history before it, the outer planets, vastly different in climate (partially due to terraforming) and beyond the immediate reach of the more populated core planets, decided that they had little in common with the central government, and sought to become autonomous. This led to the so-called “Unification War”, much like America’s own Civil War: a smaller population who feels that their needs are being unmet decides to govern itself via war with the greater power. And, like the Civil War, the "Browncoats" or independent armies, lost to the greater Alliance, and it remained a single entity.
However, this was not without great cost to both sides, after the pinnacle battle, the Battle of Serenity Valley. This was the decisive point upon which the name of the Firefly-class ship, Serenity, is based, as the captain, Malcolm "Mal" Reynolds and his second-in-command, Zoë Washburne, both participated in this effort on the part of the Browncoats.
In addition to the parallelism to America’s own war history, Firefly shows a direct reference to the lawlessness and vigilante nature of the American Westward Expansion. Again, we see an example of the patterns of civilization repeating. A population of people expands out from the core, but since the population is extremely small compared to the vast amounts of space inhabited, the government, while technically still a power, is a relatively useless one in the outskirts of humanity given the sheer magnitude of their territory. As a result in both cases, lawlessness ensues. Separate self-proclaimed lords gain dominion over plots of land and areas, and personal honor (or apparent lack thereof) is the only power that matters. Vigilantism becomes the only way of handling an issue, as the central government is too far away and doesn’t know enough about the land it is governing to do much about it. Firefly is based around the same principle, presented by the same situation, only on a greater spectrum.