A Brief Overview of Everything (Cliff Notes version, third edition)

[Namagomi]

[Earth]
The Earth of today is a lifeless shell compared to prior to one hundred years ago.  After the Great Impact, it has been reduced to a dark, dead world; a twisted image of its former self.  Even from orbit, it looks unrecognizable; a super-thick cloud of dust covers the entire planet, blocking out sunlight and warmth.  The result is a cold, dead planet, littered with uninhabited ruins of the time before the strike occurred buried underneath layers of snow and ice. It now exists primarily as a means to acquire resources.  The Lunar Federation originally staked a claim on the Earth and its resources, running several mining operations on a regular basis, but the Martian Commonwealth's arrival to acquire its own resources from the dead planet was enough to spark a war between the two colonial powers; one that the third power, the Jupiterian Sovreignty, eventually joined in on.  As of current, the Great Impact serves as justification for the White Cross Rebellion's ideals...

[Colony-States]
Since the Great Impact, the minority of the human race that escaped eventually settled into three colony-states; those on the moon (Lunar Federation), those on Mars (the Martian Commonwealth), and those on Jupiter's moons (the Jupiterian Sovreignty).  Each of these colony-states has developed to the point where they could be considered planetary nations, and in this day and age, are the only bastions of humanity left--now at war with one another, and temporarily allied to deal with a third enemy.

[Lunar Federation]
The nation formed from the oldest successful colony, expanding vastly outward with the influx of refugees as of the time of the Great Impact, among those to settle on the moon were high-ranking executives and the like those who had hoped that the impact wouldn't be as apocalyptic as it was, hoping it'd be viable to return to Earth and reclaim what was theirs soon after.  Unfortunately, it didn't turn out that way.  Regardless, they soon laid claim to terrestrial resources, and claimed the Earth itself as their territory, selling off the resources to the other colonies at inflated prices.  The MC attempted to set up its own mining ops on the Earth to skirt their scalping attempts, blatantly ignoring warnings--and as a result, the LF started attacking said operation sites.  Thus began the intercolonial war.

[Martian Commonwealth]
The martian colonies, at the time of the Great Impact, were arguably the most well-suited for holding more people, intended to be a permanent establishment to eventually grow until the planet was either terraformed or the colony covered the entire surface.  As such, the majority of escapees headed there.  As of now, it's the most populous colony, but not without its issues; cut off from earth and not able to effectively mine the asteroid belt, it was, for a while, not able to acquire resources aside from garnering a further debt toward the Lunar Federation.  This led them to eventually strike out and perform their own mining ops, sparking an intercolonial war that eventually went both ways.

[Jupiterian Sovreignty]
The colonies on Callisto, Ganymede, and Europa were originally created as work/prison colonies, and later treated as the dumping grounds for the politically undesirable; in a sense, functionally the middle of nowhere, stuck on moons of ice orbiting a planet far, far away from Earth, set to work mining both the moons they were colonizing, as well as the asteroid belt; an extremely risky operation in and of itself.  Needless to say, thanks to this, they hold a lot of enmity towards Earth...and in turn, the people who escaped the Great Impact.  Still holding less than good relations with both colonies, this resentment surfaced in particular by their surprise attack during the Intercolonial war.  They remain surprisingly strong as a force, with a conscript military force in addition to their regular army, and regular access to resources from the asteroid belt--something unique to their faction in particular.

[White Cross Rebellion]
A recently-formed faction, the White Cross Rebellion is a group of religious extremists who believe that humanity was divinely ordained to perish during the Great Impact.  Equally opposed to all of the colony-states they attack without warning or discrimination.  No central base has been found as of current, but it is suspected that it is on the inner side of the asteroid belt, given the frequency of attacks on the LF and MC compared to those on the JS.  They fight with impressive fanaticism, but are comparably lacking in both modern weaponry and military expertise.  Nonetheless, their actions have resulted in a cease-fire of the intercolonial war, as all three colonies focus their efforts on removing this nuisance first.

[Active Frames (AF)]
Active Frames were originally not designed as military weaponry so much as they were as multipurpose utility vehicles, derived in turn from older combat walker designs from the military of Earth when it was still in its prime.  However, once it was evidenced in an infamous crime in the MC that such could be used as dangerous weapons, even when not armed, it became quickly apparent that AFs first became useful first for police use, and then for military use.  Operational life was previously limited, requiring direct power feeds or on-board fuel, until not long before the Intercolonial War--the advent of microfission reactors and the adaptation of such led to a lifespan that lasted long enough for extraordinarily long operational ranges, lasting until the fuel gives out and requires replacement.  Nowadays, however, they are outclassed by NFs, and compared to these newer machines, most AFs are slower and more difficult to control.  Some notable pilots prefer to stick to their AFs, and are not to be underestimated.

[Neural Frames (NF)]
Neuro-Active Frames, more commonly known as Neural Frames or NFs, were a breakthrough development in the intercolonial war, brought about by the efforts of the Lunar Federation.  The difference between these frames and their predecessor is the method of control.  Eschewing the arrays of levers, pedals, and buttons for a direct neural link-up, a greater amount of multitasking is possible with these machines.  While it was expected at first by the LF that the machines would give them a dominant edge, a single problem prevented them from becoming the end-all of warfare; they had nobody with actual combat experience who could use them in combat to begin with.  They had fielded combat aces in the first production models, and while they were a terror for the Martian forces, and even gave the Jupiterian forces pause, it wasn't long until NFs were captured by both of the other forces, reverse-engineered, and adapted to their own, fully disseminating them amongst all sides of the conflict.

[Genetically Altered humans (GA)]
GAs are a relic of Earth prior to the Great Impact.  Genetic modifications were used to create more specialized humans for varied tasks--military and civilian.  Often of corporate origin, these humans were modified in-womb.  The original 'models' looked exactly like normal humans, but due to the altered genetics, created problems when attempts to interbreed occurred.  Following this, pressure from both religious and special-interest groups led to the inclusion of cosmetic changes designed to mark the people as GAs.  While there was heavy discrimination of them on Earth to the point of them being considered no better than animals by some, GAs who were created since the Great Impact mostly do not suffer such stigmatization--though some people still hold low opinions of them.