A familiar or diminutive of "covenant", referring to member of one of the several alien races that comprise "The Covenant" in Halo and Halo 2. Usually used as a term of endearment.
The video clip showed MC smacking down a pile of covies with style.
Slang terminology in Halo 2, referencing the Beam Rifle, the Covenant version of the sniper rifle.
1. Here, give me the Covie.
2. (shoots other player) The Covies down...