The Alliance
In the Firefly television series, the Alliance is a powerful government and law-enforcement organization that controls the majority of territory within the known universe. Originally composed solely of a number of "core worlds", several years prior to the show's timeframe the Alliance fought the Unification War to bring all colonized worlds under its control. The Independent Faction (Browncoats) wanted the outer worlds to remain autonomous and attempted to resist Alliance control. The war raged for several years, resulting in heavy casualties on both sides, until the Alliance emerged victorious. An armistice was signed between the Alliance and the Independent Faction, thus ending the war and securing Alliance control over the entirety of the system.
The Union of Allied Planets
NAME
The scripts for the pilot episode, "Serenity", and the first-aired episode, "The Train Job", refer to an "AngloSino" flag on the IAV Dortmunder and on the stolen boxes. However, the term AngloSino Alliance was never used in an actual episode or film; the phrase Union of Allied Planets is explicitly mentioned in on-air dialogue in the episode "Ariel", so it can be assumed to be the formal name of the Alliance.
HISTORY
After Earth's natural resources were used up generations ago, mankind abandoned the planet (which now exists in myth and legend as "Earth-That-Was"), and moved out into the stars. But, mankind held onto the tenets of culture and civilization in the exodus, carrying with it those things both material and spiritual that make us human.
Relatively little is known of the early history of the Alliance (such as the exact date of the exodus from Earth, and the reasons why China and the USA allied themselves with each other). The Alliance flag, seen in the original pilot episode, is a blending of the United States and People's Republic of China flags (two versions of this flag, one with 13 stripes and one with five stripes, appear in the series).
At the Battle of Serenity Valley (the last major battle in the civil war, based on the Battle of Gettysburg), both the Alliance and the Browncoats suffered heavy casualties, particularly amongst officers. Survivors from both sides were stranded on the battlefield until the Alliance was able to send a fleet of medical transports to rescue them.
The day that the civil war ended is known as "Unification Day" (often abbreviated to "U-Day") and is celebrated as a holiday throughout the Alliance. Alliance military officers like to drink a toast to Unification Day and enthusiastically encourage others to join in the festivities.
UNIVERSE
The two worlds that make up the "core planets" (the first worlds to be terraformed) are Sihnon, a mostly East Asia-themed planet, and Londinium, a world with mostly American and Western Europe influences. The alliance of the two worlds leads to up a multi-racial, multi-ethnic, and multi-religious universe.
The Alliance seems to have some elements of a monarchy. In "Serenity", Malcolm Reynolds (Serenity's captain) said "I'd like to be king of all Londinium" and many of Inara Serra's customers are Lords. However, "King of all Londinium" may just be a catchphrase (ie, "king of the world" in modern usage) and Lord could merely be a positional title (such as modern judges in Britain). In Serenity, the movie set in the Firefly universe, it is revealed that the Alliance is run by a branch of the government called the Parliament.
It appears that this Alliance was a melding of the People's Republic of China and the United States of America. Generally, the Alliance is rather authoritarian, although Joss Whedon, the series' creator, has said this is at least partly due to the fact that the show is seen from the viewpoint of those hostile to the Alliance. Whedon himself admits that sometimes, the Alliance is like the USA in World War II: doing very good things, helping people, spreading democracy. At other times the Alliance can tend towards black ops and power-grabbing, although rarely more so than any other real-world democracy.
In any case, the Alliance is far from the traditional totalitarian government such as the Galactic Empire (Star Wars) and the Federation from Blake's 7. The Alliance is also similar in concept to Jerry Pournelle's CoDominium, that a democratic and communist superpowers would form an alliance.
It is a government run by bureaucratic rules. Corporate influence is high, the prime example of "Blue Sun", a powerful corporate conglomerate Whedon has compared to "Coca-Cola or Microsoft" and which owns "at least half the government". A lesser example is the Weyland-Yutani corporation of Alien fame, whose logo can be seen on certain Alliance weapons. In Serenity, the Alliance also relies on local security companies to serve as the Alliance presence.
Due to the melding of American and Chinese influences in the Alliance, most people in the Firefly universe are equally adept in speaking both English and Chinese; some characters on the show speak Chinese at times (usually when using obscenities, so Joss wouldn't have to bleep anything out and ruin the suspension of disbelief), and many signs are printed in both English and Chinese. Additionally, during the episode "Out of Gas", Serenity's warning messages over the intercom are repeated in both English and Mandarin.
ALLIANCE MILITARY
The Alliance operates a massive fleet of spaceships, resembling huge floating cities, that act as both military and police for the distances between the various planets of the Firefly Universe. Alliance ships have the registry prefix IAV (Interstellar Alliance Vessel). Examples include the IAV Dortmunder and IAV Magellan. The pilot episode of the series reveals that the large city-ships carry smaller craft referred to as 'gunships', though the gunships themselves are never identified and their specific characteristics are never revealed. In the episode "Bushwhacked", we learn that Alliance ships have nurseries, suggesting that there might be even more civilian facilities aboard.
In the film Serenity, we see a fleet of sleeker, more streamlined warships, suggesting that the Alliance has a wide variety of space vessels for various purposes.
Alliance ground troops are nicknamed "purple bellies" (in contrast to the Independent "browncoats"). They wear armor similar to that worn by the Mobile Infantry in the movie Starship Troopers (the makers of Firefly used leftover costumes from that movie). Crewmembers on Alliance starships wear gray uniforms resembling those worn by Imperial German Army from the First World War; officers and enlisted crew are identically dressed (except for headgear: officers wear hats, enlisted crew wear berets). In Serenity, Alliance crew members wear blue uniforms.
The exact structure of the Alliance military, such as its rank system and branch organization, is not identified within the series or the film. Some Alliance officers have been seen with naval ranks, such as Commander, and others with ground-based ranks such as Colonel and General.

