It is supposed to re-soften and stress relieve the brass, to stop it becoming work hardened and brittle after many times of being "super heated" momentarily as the round is fired (the brass doesnt stay hot enough, for long enough during use). By heating the brass for the appropriate length of time in the correct manner, the case becomes more maleable again and is more resistant to splitting after several uses. This is especially important around the case mouth where it is constantly being flared, crimped and shot. Like bending a piece of steel back and forward, it gets weak and likely to break due to metal fatigue.
FYI: The only way brass becomes brittle is from "work hardening". The only way to soften it to keep it from splitting from being brittle is by heating it to the proper temperature...lenght of time at that temp is not a factor in the softening process.
The temp that brass is heated to in firing is not hot enough to anneal the brass.
Most of the work hardening comes from sizing, expanding, crimping the case during the reloading process.
It is not necessary to "stress relieve" the brass.
Brass can be over annealed (becomes too soft) resulting in prolapsed shoulders when pressing in a new bullet.
Brass can be annealed more on one side than the other, so the case must be rotated if a flame is used.
The brass case has three different zones that have different hardness. The neck must be soft, the head (where the primer is) must be fairly hard and not subjected to annealing...primer pockets will enlarge upon the first firing after annealing releasing gas to the rear, and the head may fail altogether. That is why persons who use the lead pot method hold the head of the case in their fingers...to insure that it does not get hot enough to anneal. The center portion of the case is usually not as hard as the head, or as soft as the neck of the case.
In most methods of annealing the case necks, there is some quenching method to keep the heat from being conducted to the body or most importantly the head of the case. Quenching does not change the properties of the brass; if you did not quench and let the neck cool on its own, it would still be annealed...but the case could then be dangerous to shoot as explained above.