During the twilight before the civilization-wrecking warfare that defines the modern age of Battletech, a number of folks saw the writing on the wall and took their toys with the intent to go home with them. Home was just as happy to blow up its own nose to spite its face, so they took their toys and voyaged through space for months on end with no real goal. People in Battletech get straight A's in dramatic action, but straight 'incompletes' in thinking things out. One mutiny and several suspected cannibalizations later, they found a quintet of stars, each with a habitable world, in convenient proximity to one another.
As a general rule of thumb, everything important is named 'Kerensky.'
These weary travelers rested their heads and life was good until someone started taking bets as to which state they had abandoned was currently blasting the others into the stone age at a slightly faster pace than the rest, and then someone had a baby and everyone wanted to give them advice despite having no common cultural framework for doing so.
Then, those refugees began to blow each other up and wrecking what little civilization they had on these five barely colonized worlds.
But some of the guys saw the writing on the wall and left their nascent homes to travel into the darkness of space--with no real plan--to avoid the chaos and devastation of civilization.
Either Battletech is the slowest Monty Python reference with "technological decline" replacing "fell into the swamp," or it's a prophetic iteration of the "Yo Dawg" meme featuring a guy that Xibit heard liked "exoduses from a collapsing civilization."
Yo dawg, we heard you liked tired memes...
As one might expect from fiction featuring giant robot war machines, politicians shooting more lasers than legislation, monarchies spouting unironic democratic values, and prevailing technologies that prohibit women from wearing anything more than underwear in the midst of deadly combat, those who exodused from the exodus secluded themselves for twenty years on harsh worlds where they trained relentlessly to both become better warriors through the honing of their martial skills and become worse warriors by believing those skills would form the foundation of an effective, equitable government. Those guys became The Clans.
There were originally twenty Clans, most of which were named after wacky animals found only in the second group of exodus worlds (known as The Kerensky Cluster).
The Clans use warriors genetically constructed from the genes of successful(Bloodnamed) warriors of the previous generation as both their main-line troops and as their leadership (therefore creating a collection of states governed by a collection of pedigreed warrior-leaders to replace the collection of states govered by a single pedigreed warrior-leader they had just left behind.). However, other 'Freeborn' citizens of other castes (roughly translated to 'slave caste,' 'slaves with name caste,' and 'devious plot device caste''), can try out to become warriors. Since most of these 'Freeborn' die from the universally arduous training conditions, most of the remainder die from institutionalized bigotry, and those who succeed are generally armored cannon fodder, the primary purpose of allowing 'Freeborns' to become warriors seems to be the entertainment of the more sadistic members of Trueborn warriors.
Similarly, aspiring Trueborn warriors (all of them) are also put through rigorous training before they are allowed to fight; many of them die and only a handful from each class, or 'sibko' actually become warriors. The remainder wash out and are reclassified as members of another caste.
This, as do many things, varies from Clan to Clan.
For Trueborn warriors, their highest honor is to become Bloodnamed and die in glorious battle. Each Clan has twenty bloodnames derived from the original twenty warriors which founded it. Obstensibly, those warriors' genetic legacies form the foundation of that entire Clans' warrior caste (trade with other Clans and vaguely defined genetic science keep inbreeding from being a problem). Up to twenty warriors can share each bloodname at a time. These warriors are the only ones who have their genetic legacy passed on to the next generation, and they also comprise the Clan council which effectively rules the Clan under the leadership of an elected executive, or Khan.
Natasha Kerensky, because she's relevant to just about everything in this article.
Whenever a bloodnamed warrior dies, other warriors who share that name elect mechwarriors who have performed well in combat to replace them. Those warriors fight in a tournament--yes, it's called something else, but I've played enough Street Fighter to know a deadly fighting tournament when I see one and I'm not about to bullshit you on this--to see who is a good enough warrior to receive the bloodname and have their genetic legacy passed onto the next batch of vatborn killers.
Back to the (Slightly Earlier) Future
Operation Klondike was The Clan's return to The Pentagon Worlds after twenty years of absence. While the forces present had destroyed themselves enough to make a victory of 400 warriors over five planets seem feasible, there were still significant armies present to make the fight an entertaining one for the reader.
The Golden Century was the period of time that followed Klondike, during which The Clans decided to improve the universe by killing each other exclusively. During this time their Devious Plot Device Caste came up with a number of advanced technologies that their leaders took and used without even saying thank you to prove to one another that their warrior genes were superior.
Operation Revival is the period of time where The Clans invaded The Inner Sphere, planning to liberate the place they'd abandoned to barbaric warfare all those years ago with slightly more civilized warfare.
Strangely, The Clans did some reconnaissance on their target fifty years before their invasion (operational intelligence isn't usually the strong suit of a culture who thinks that being a good shot qualifies you for governance) by sending some guys along. Those guys posed as mercenaries while gathering intelligence they sent back home, realized that The Inner Sphere was central to the setting, and then did everything they could to sabotage the Invasion (In keeping with everyone who betrays The Clans, no sane person in the setting considers them traitors.). Only one Clan read their intelligence during the invasion. This means that The Clans collected interesting dividends on their intelligence mission: The Inner Sphere received a collection of top-notch Clan warriors, The Inner Sphere got a slug of advanced technology, The Inner Sphere received intelligence on The Clans, and The Clans received the blackest, most metal gift of all: absolutely nothing.
Though it explains their reluctance to engage in intelligence-gathering missions, now that I think about it.
The universe's foremost intelligence agency.
Whenever the first wave of Clans (somehow) got stalled out by the technologically inferior, less-skilled, numerically superior, well-informed underdog warriors of The Inner Sphere, they activated a second wave of Clans eager to kill things. As unimpressive as the first wave was, you could be forgiven for forgetting the names of the second wave, even if they killed you.
Finally, ComStar (the interstellar phone company which keeps legions of elite mechwarriors, the Com Guard, on their payroll because don't ask questions just go with it!) challenged them in an all-or-nothing Trial on the unassuming world of Tukayyid. If ComStar won, The Clans would halt their advance. If The Clans won, they'd be really dissappointed when ComStar reneged on their offer to hand over Earth (losers).
The universe's foremost fighting force/phone company.
Pretty much the least-martial of the insignia in the Battletech universe. Even their splinter groups throw a broadsword in there. A ??? with a trailing ??? is the wussiest thing in a universe where every other insignia is something trying to kill or punch you.
Goddamn it St. Ives, there's a reason you don't exist anymore.
Again, Sarna.net is the source for most of these images.