The absolute antithesis of what it means to be a member of a team. This term comes directly from the Call of Duty series where teammates are represented on a minimap by small green arrows. In World at War and later installments, a green arrow can be anyone outside of a player's squad.
A typical green arrow shows little regard for victory conditions, no self-preservation or communication skills, no weapon knowledge, and an overall lack of understanding with respect to basic gameplay mechanics. Always in direct contrast with "blue arrow".
Teammate: "Hey, green arrow, help me out. There is a sniper in that building, and you're right behind him."
Green Arrow: "..."
Teammate: "Why are you just standing there?"
Green Arrow: "..." (pulls out grenade)
Teammate: "Yes, at least take him out."
Green Arrow: "..." (grenade detonates in hand)
Teammate: "..." >:(
Describes a member of a team that denotes basic level of skill and communication in accomplishing the simplest of team-based tasks.
Largely in reference to Call of Duty: World at War and subsequent titles, with blue arrows on the minimap indicating members of the player's own squad - usually the only competent teammates in the game.
Always used in direct contrast of "green arrow", which is the exact opposite of gaming excellence.
Squad Member: "Help, I'm down - can someone revive me?"
Blue Arrow: "Sure. By the way I heard the shot, sprinted across the map, gutted the man who dropped you plus two of his friends, dove on a rogue grenade, and called in a gunship for cover. You know I got your back."