I've tried to watch this a few times because it seems up my alley, but the way they drop you into the universe in the first couple of episodes just fails to keep my attention and then I end up missing too much stuff amidst my distractions to really get a feel for it.
It's probably a failing of my own attention span rather than the show, but alas I haven't managed to get into it despite numerous attempts.
It's hard to follow in the first couple of episodes because so much happens.
Earth is the big power of the solar system. They have the numbers, the finances and a lot of political clout in the system. There are a number of political players from Earth featured in the show. Their colour is blue.
Mars is technologically way ahead of Earth and have stealth technology. Mars is a bit like what Russia was to the USA in the cold war. They're technologically way ahead of Earth in stealth technology. They were founded by a bunch of scientists and engineers and value intelligence highly. They don't have the raw numbers that Earth has, but they do have the best military technology. Their colour is red.
The belt is divided into a number of factions. The belt is made up of Eros (the largest asteroid in the solar system), Ganymede (a moon off Jupiter), a space station who's name escapes me (where they're building the Mormon generation ship) and a bunch of other small factions, outposts and groups of people. The belt is notionally not governed by a united government, but the OPA is a political alliance that has a big following in the belt. They are disorganised and living on the edge. They're identified by their South Africanish accents. The belt is hard and the people who live in the belt face death regularly.
The main characters are James Holden, who was originally from Earth but is the vice captain on an ice hauler in the belt, Chrisjen Avasarala a powerbroker in the Earth government, Detective Miller a cop on Eros station. There are a bunch of other characters but these are the main three that you should know. Holden is the lawful good, Miller the chaotic good, Chrisjen the lawful neutral.