"Collection of
militaristic pseudo-
tribal groups descended from military forces that fled the
Inner Sphere hundreds of years ago. Technologically superior to the inhabitants of the Inner Sphere, the Clans have returned to 'liberate' the Inner Sphere from the 'barbarians' who rule it".
- MechCommander manual, FASA Interactive/MicroProse
To be more specific: Nicholas Kerensky's father, Aleksandr Kerensky, fled the Inner Sphere in late 2780s and the Clan invasion started in 3050.
The Clans are not exactly the "bad guys" of the BattleTech; They aren't more evil than anyone else in the universe, even if the Inner Sphere propaganda tries to hint that way.
They are just radically different from the world as we know it; They are conformists, they have a caste system, they breed their warriors artificially, they control their gene pools with stress on one's lineage (eugenics program), and have interesting honor ideals.
The Clans have two political factions - the Wardens that think they should protect the Inner Sphere from outside threats, and the Crusaders that think they should just invade the IS and liberate them.
The Clans:
The Fallen:
See also: BattleTech