I'm going to take maturity from it's context in other things and apply it to us. When something is mature, like an animal, it means that it has hit it's plateau of physical growth, and there's not going to be any more rapid change or development in that respect. When something matures like a drink, it means it has time to age and season itself properly. It has taken the time to settle and absorb all the flavours in it, had the time to to change from it's mixed, messy origins into something of value (else why would you let it sit for so long?).

And if we apply this abstract notions to people, I get the point where we have stopped rapidly developing, and the point where our life experiences have given us a perspective that is balanced, because the many aspects that build life and perspective have settled into something valuable. Wisdom and maturity are very similar in this respect, I think.