Armitage is Zimmer's imposing bodyguard, a quiet individual. He will defend Zimmer to the death. Armitage is actually an android, or synth, much like the replicant. Armitage has the same schedule as Zimmer; he sleeps in the same room and eats the same food - not because he has to, but because he has been programmed to replicate human behavior as closely as possible.
Despite his status as an android, and his claim that he could "break your neck like a chicken bone," he is no more durable than the average human.
If he is killed, one of only four android components in the game can be found on his body (of the other three, one is on Zimmer, one is given to the Lone Wanderer by Victoria Watts, and one is on Pinkerton).
Killing Zimmer before he tries to leave with Harkness in The Replicated Man quest will result in Armitage living forever in the Rivet City market.
He can be killed with no loss of Karma, and killing him with Harkness' permission will not cause Rivet City's security to turn hostile toward the player character.
"That's close enough. Keep your hands where I can see them."