"Release Spirit" refers to when upon death, the act of a player releasing their spirit form (a ghost or Wisp) from their corpse and allowing it to spawn at a nearby graveyard.
In instances and other occasions while grouped, the recommended behaviour is not to release until all mobs are dead, or all players are dead (or cannot continue combat any further).
Releasing prematurely has these disadvantages;
You will not be able to loot or roll on loot on mobs that die after you release.
Any players trying to resurrect you will have a much harder time finding your corpse.
If you died and ran back to the instance to rez before the healer could rez you in place, you will have to navigate your way back to the main party. If you are unfamiliar with the instance or the mobs have respawned, you will slow down the group as they must work to retrieve you.
Some forms of resurrection spells (eg Goblin Jumper Cables) have a much lower chance of success (and may not work at all) if you have released to the graveyard.
You will not receive the achievement for an instance if you have released, and you are not in your corpse when the final boss is killed.
If for whatever reason you can't release your spirit by conventional means there is a Slash Command that will release you:
If there is a total wipe with no ability to rez in place, having everyone release and run back at once will simplify dealing with any wandering patrols or respawns.
Using a self-resurrection spell such as Soulstone Resurrection or Reincarnation while there's still a chance that someone will be able to rez you conventionally after combat is considered wasteful.