Respawn is a video game term that refers to "coming back to life" usually in a multiplayer deathmatch or similar scenario. It's mostly used in first-person shooters. The term "respawn" was first used when Doom was originally released in 1993 for Mac and PC.
Depending on the parameters of the match, players generally respawn after having been killed, or fragged, to continue the match. In many games, enemies will continue to respawn after killing them.