Disclaimer:
I am not a metallurgist.
I did not play one on TV.
I did not stay at a Holiday Inn Express last night.
Here goes my understanding of annealing.
Brass, and other metals, are a crystalline structure.
When heated, the crystalline structure 're-arranges itself' (non-technical term)
in order to create a strong yet soft, or ductile (technical term) structure.
This allows for the expansion, and contraction of the case when loading as well as firing.
Each time the case is fired, it looses some of the ductability. If not re-annealed, the case will eventually split.
This is because the crystalline structure has re-alligned itself, and created a less ductile, or work hardened metal.
For a completely technical description
Try this explanation form Wikiedia
Someone please correct me if I am mistaken on any of this.