This article is from the Final-Fantasy and other Square Soft Games FAQ, by firstname.lastname@example.org (Nick Zitzmann) with numerous contributions by others.
When you've mastered a materia (raised it to it's maximum level by
collecting AP), it stops growing. However, a new materia of the same
kind will appear in your Materia menu: however, it will be at level 1
with zero AP. While you can usually find/buy more materia of the same
type, there are some cases in which there is only one materia of that
type (say, Comet or Odin) in the entire game. In that case, you have to
master that materia if you want to get another one, via the 'birth'