What do salmon and deathmatchers have in common? They both respawn.
Respawning (in a video game) is when an item, enemy, or player reappears after having been picked up or destroyed in a video game. Alternately, respawn can be used synonymously with respawn point, which is where an item, enemy, or player appears after having been picked up or destroyed.
Respawn is taken from "spawn", which, in this context, is when a new element, be it player, item, or enemy appears in a stage. While the terms "spawn" and "spawn point" predates first person shooters entirely, the actual first use of these two older terms is unclear. (I've found them in MUD documentation that predates Doom.) Respawn, on the other hand, originated with Doom, with the meaning used to the current day. The term has since been retroactively applied to older genres of games; enemies who would once have been referred to as "reappearing" are now said to be "respawning". An example from common video game design flaws, referring to aging platformers: "Kill an enemy, move a few game meters, and come back to where the enemy spawns. It will have respawned because of the healing power of offscreen." (yerricde) To date, the term is most commonly used in the genres in which it originated: first-person shooters and MUDs (as well as MUD-like MMORPGs).
When referring to players, respawning tends to be at the spawn point as far from the enemy as possible (and with the minimum possible armament - traditionally this is a pistol and a melee attack) in most FPSes, or in a base in capture the flag or other team based-scenarios with home bases. In other, however, enemies and items tend to always respawn at the same spot, in any genre of game. In FPSes and MMORPGs, this tends to lead to people camping the respawn points, looking for items, powerups, or enemies. In other genres, this information is less useful, and players often exploit it only to destroy enemies as quickly as possible, if at all.
Player respawning was once an iron-clad genre convention of competitive multiplayer, but, as deathmatch FPSes lose their control of the genre, more and more games have no player respawn, looking for a more realistic experience. A textbook example would be America's Army, where a lack of respawn is used both to give more of a feeling of being one good shot away from being dead.
See also: camping, spawn