Two players fight two Zombies in E3M2: The Vaults of Zin

In a co-op game, you and your friends work together to finish the level. When one person exits, everyone else exits too, wherever they might be. If you are killed in co-op, you reappear at the start area, and have to catch up to your buddies. Use Talk to find out where they are. See the Multiplayer options on the Main Menu for more info.

Quake Manual

Cooperative or Co-op is a Game Mode present in Quake and Quake 2 where multiple players can labor together to finish a level containing Monsters. Unlike Single Player, dying does not equate losing. Instead, the dead player will respawn, only sans the items acquired during her or his progress in the current level. Friendly fire may still injure fellow players, depending on the server’s configuration. If Teamplay is activated and the players wear the same color of pants, they shall be unable to injure one another.

While items do not respawn in Cooperative, some items will remain totally independent of who acquires them. Eight players can all acquire the same weapon or key and it shall still exist. In Quake Powerups, 15 Health or 25 Health, Backpacks, and Ammo do not respawn; but both Weapons and Ammo can be acquired from dead players. When playing a Cooperative match it's important to share ammo and health with other players.