Respawning is an automatic function performed by the server in Quake, where certain variable entities in the Quake World are spawned a certain amount of time after they have been changed somehow. For the most part the entities are either items that have been taken (or moved), or players (after they have been killed).
With deathmatch mode 2, 3 and similar spinoff's, items do not respawn.
Some respawn times:
Players: straight after death. In duels there is usually a forced respawn time.
Weapons: 30 seconds.
Armor: 20 seconds.
Ammo: 30 seconds.
Megahealth: 20 seconds after the player who picked it up's health has dropped below 100.
Quad Damage: 30 seconds after it wears out, beholder has been killed, or it disappears (if it gets dropped)
Pentagram of Protection: 5 minutes after being picked up.
Ring of Shadows: 5 minutes after being picked up.
Respawning is closely related to item camping.