Ok here's how. You FL size a case which now fits slopply in your chamber. You fire said case and it expands to fit your chamber. Also the brass, upon firing, flows forward somewhat. Depending on the cartridge trimming the case may be necessary after a few firings.
Now you take that same case again and run it through your FL sizing die. So every time you FL size and fire that case you're contracting and expanding the brass, hence work hardening it.
Just running a case that was fired in your chamber enough just to allow proper chamber (.002" shoulder bump) reduces the working of the brass. Also like I noted before, with a belted case which head spaces off the belt, doing a shoulder bump will reduce case weakening in front of the belt by reducing case stretch.
And when I said annealing helps I meant just what you said. It relieves the work hardening.