The Setting
The show is set in another solar system which had plenty of planets and moons which turned out to be ideal for human colonisation. Many of the places visited in the show are mentioned as being orbital moons of gas giant planets for example. The colonisation was done straight away or after a terraforming process. The reason for this great expansion of mankind is explained by the phrase "Earth got used up".
In the new solar system, there has just been a large civil war between the alliance and the independant "Browncoats". The alliance were a group of close inner planets who had decided that the entire system should be under their rule. The alliance won and are now the only major power around. This has a major bearing on the show as the captain fought for the Browncoats and is bitter over the Browncoats defeat.
There are no aliens in the show, they are simply not there. The are also very few Computer-Foo effects, the technology is just taken for granted. This is understandable as it is set quiet a bit into the future. It also makes for good storylines as the writers had to focus on the inter character drama rather than using dazzling effects as a distraction to dodgey script.
The show is primarily shown from inside the Serenity ship and develops the nine very well choosen characters.
Firefly & Serenity