Warning: This definition may contain spoilers from any number of Games Workshop novels or source books.
Primarch: The Primarch's are genetically engineered super-humans created by the Emperor in M29 and based on his own genetic code. They were created to help in his Great Crusade. When the Chaos Gods learnt of these super-humans and found themselves unable to destroy them they were scattered across the galaxy, landing on many distant worlds. Each Primarch was found by the local community and brought up as one of their own, although they grew, developed and learned much faster than normal children.
Each Primarch became a great warrior and leader, taking power on the world he had landed on. Once The Emperor had arrived to return the Primarch to his side on Terra, each was used as the basis gene-seed for one of the founding Space Marine Legions. Due to this close link and the upbringing of the Primarch on his homeworld, each Chapter took their character from that of their Primarch, and hence from the population of his 'homeworld'. Nearly all Primarchs are known to be either dead or lost in the warp, while the location of the others is subject to many wild and hopeful rumours.
By M32 onwards, most Primarchs had either been killed in the Horus Herest or else died during the millenium.
Source: Unknown by unknown