what is it and the method? Purpose?
Metal is comprised of crystals; they are essential to its character. Every time you bend the metal, the crystals get further deformed and broken. Eventually the metal gains strength and hardness, but loses its property of malleability and will break when deformed, rather than bend.
Annealing is the process of heating the metal to give the atoms enough energy to restack themselves into new crystals. This will restore all the properties of toughness and ductility to the metal, and lower the hardness and strength. Obviously, it won't allow cracks to heal themselves or anything, but so long as the metal wasn't physically broken, it should be fully restored.
The basic method for 70Cu-30Zn brass is to heat the metal into the annealing range of 300-800C for a time, then let it cool. Times range from less than a second to several hours. Lower temperatures mean longer times.
For cartridge cases, the added stipulation is that you only want to anneal one end. The case head must remain at full strength to survive the firing process. Because of this, only short annealing times at high temperatures are feasible. I am still working on proving this, but I believe that 600C for about 4 seconds is the neighbourhood we should be looking at.
Annealing is not universally necessary or practised by reloaders. Part of the reason for this, I think, is that the process is very poorly understood by most people, and often done improperly. Much of what is written in reloading manuals and gun magazines is flat out wrong. The article on annealing on 6mmBR that someone will no doubt link to soon is about the only thing I have ever seen on cartridge case annealing that is worth reading.