Just take in mind it's not -exactly- like Firefly. That's just the closest comparison I could think of.
There are basically four tiers to the system; Civilian, Corporate, Government, Military.
Civilians are at the bottom of the ladder, and are frequently lumped with decades old technology. This is mostly because the plans for that technology were lost, so the Corporations aren't really any better off. The Governments and Militaries that remain have the best technology available.
In the far future, something went wrong. Very wrong. Governments across the universe collapsed. For reasons lost to the depths of time, during that 'dark' age, the Corporations seized control.
There are four levels of Corporation;
Continental Corporation - spans only a single continent on a single planet.
Planetary Corporation - spans an entire planet and has control over the majority of it's populace.
Governmental Corporation - spans several planets in what is called a "Sector".
Mega Corporation - spans several sectors to control one or more "Quadrants".
Sectors usually hold half a dozen planets, and their borders shift regularly. Quadrants can hold upwards of 20 planets and their borders are defined by the owner.
Governments have taken a back seat, and mostly deal with more civilian matters that are escalated to the best suited Corporate authority.
The only notable surviving Government is the Terran Republic, still based on Earth. They are perhaps a shining bastion of hope and technology for those tired of life under the corporation's heel. The Terran Republic Navy is far superior to any of the Corporate Fleets in terms of technology and training, but their numbers are low. Were a Terran Destroyer to slice a Corporate Frigate in two with an ion beam, another three would leap to replace that frigate.
Many civilian populations, brainwashed by endless streams of corporate propoganda, percieve the Republic as evil, soul-sucking, baby-devouring hell-spawned fiends from beyond. The Republic do not do much to counter the propoganda, but have been noted for keeping a large "Corporate-Free" zone around the Sol system. Any ships with an active Corporate Transponder are destroyed as soon as they are detected. The Sol system, birthplace of humanity, is the only system under the Republic's control. However, thanks to the Republic's advanced technology and the extensive use of artificial intelligences and remotely controlled systems, it still retains enough military clout to fight off Corporate invaders and pirates.
There are four main powers to the universe; Corporations, Governments, the Pirate Factions, and the Anti-Corporate Coalition.
Fifth on the list and rarely spoken of are the few "Free Worlds" that are lawless planets where the man (or woman) with the biggest gun has the biggest say. Some are used as bases or even headquarters by the pirate factions, and several Free Worlds also host the Anti-Corporate Coalition forces in exchange from protection from the money-grubbing CEOs. Each free world is considered as a unique entity and no two free worlds would ally, as it would lead to them becoming one of the things they loathe the most.
Whilst shunned by most Governments and on fairly shaky terms with most Pirate Factions, the Anti-Corporate Coalition is a fairly large group of men and women devoted to bringing about the downfall of the Corporations and restoring order to the galaxy. They are meant to be similar to the Rebel Alliance in that they believe they are doing The Right Thing and sticking it to The Big Bad. Whilst their goals are noble, the Governments are too weak to support them (though many secretly aid the ACC wherever possible) and the Pirates too interested in out-right theft from the corporations compared to the destructive tendencies of the Coalition, the Coalition rarely manages to make any major breakthroughs. Here and there they may sabotage the odd manufacturing center, but they are little more than a small thorn in the side of several giant entities.
Rambling post. Probably doesn't all fit together because I have a headache, but it should make enough sense.