the first three toy story movies have this incredible metanarrative about how Andy's toys are to Andy as Andy and all the toys are to Pixar's creators. the first movie is simple and tells a story about story telling with toys. the second one is where the metanarrative is introduced, and it explores what it means for a world to become static and unchanging with the collector and the prospector trying to create a "perfect" world but that perfect world requires no one to change or grow. in it, there will be no stories. the third is my personal favorite of this triptych exploring what happens when you age out of playing with your toys. for Andy, he goes to college and won't be bringing his toys with him, for Pixar most of the original creators were retiring. For the toys though they must confront death: the death that if no one tells stories with them, then they cease to be alive. and the great emotional payoff for the whole series is that what keeps our old stories alive is teaching story telling techniques to the next generation and letting them tell new stories with them.
and then they made a fourth one which is a ver good movie but not a very good toy story story