Annealing (softening) is the opposite of tempering (hardening) Most people have heard of tempering steel, so let's talk about that for a moment. Steel is tempered by raising its temperature to a point that its grain-structure is altered, then permanently held there by rapid cooling (quenching). If you heat tempered or forged steel to that grain-altering point again, then let it cool slowly, it will be annealed, or softened.
Brass differs from steel in how it is hardened and how it is annealed. Brass can only be hardened by work-hardening and only softened with heat. Steel can be hardened or softened with heat.
Brass is hardened by working, drawing the metal, expanding and contracting it. Cartridge case manufacturers do this in production to give you a strong case that will stand up under firing pressures. They then anneal the case neck and shoulder to soften the area that holds the bullet and expands into headspace. You get a strong cartridge that releases the bullet smoothly and then expands against the chamber wall to seal the pressure spike.
After several firing and resizing/ reloading cycles, (5 to 6, sometimes less) the brass necks become work-hardened, and won't release the bullet evenly or expand tightly to seal pressure. This results in lower velocities and inconsistent shot placement. Some of your brass will release at different times than others. Uniform bullet release (neck tension) is one major key to accuracy.
Here you can see the line of soot stops half-way down the neck, below that it is sealed. This is the first firing after annealing.
If the neck/ shoulder area is hardened, it is more prone to splitting or poor performance. This is what happens with repeated use.
This is why we anneal our cases, BUT ONLY THE NECK AND SHOULDER! Annealing the lower case body results in a dangerous soft-cartridge condition that can explode and injure the shooter.
Be aware that like reloading, annealing takes a certain amount of skill and common sense.
If you can reload your ammunition, you can anneal your cases.