One of the great triumphs of the now complete Toy Story series is the creation of a imaginary toy psychology, with desires, fears, neuroses, and stages of development. Toy psychology isn't just a projection of human psychology onto plastic objects - it stems from the unique relationship of toys to growing child owners, always threatening to lose a favorite toy, to replace one treasured plaything with another, or to grow too old to play with toys altogether, and always unaware of his toys' self-consciousness.
The Toy Stories chronicle the better part of the life of Woody the cowboy doll, a favorite toy of owner Andy, and the audience's primary window into toy existence. Woody's difficult maturing process is not primarily a matter of learning what his purpose is in that he is a unique toy called Woody, but in learning what his purpose is in that he is any toy at all. He faces the temptations of eternal life in a museum and endless but shallow affection from rotations of small children at a daycare center, but reject each of these, deciding that because he is a toy, his purpose is to serve as the object of an owner's imagination and affection. This is something that Woody knows implicitly at the beginning of the first film, but a belief that the crises of each film call into question, and one that he must eventually make a choice to follow. It is often hard for a toy to pursue that purpose. It carries the risk of abandonment and decay. It is nevertheless the right thing to do, and the only means to a satisfying life for a toy.
I think that this notion of purpose is unusual in contemporary cinema. There are many contemporary films in which characters struggle to find their purposes, but these are usually struggles to find one's purpose insofar as one is such-and-such a person and not some other person. There is very little investigation of the possibility that there is a purpose that all human beings ought to try to fulfill simply because they are human beings. The only markers of "the good life" are then autonomy and authenticity.
Christians of course believe that humankind does shares a purpose, well stated in the Westminster catechism, "Man's chief end is to glorify God, and to enjoy Him forever." Many ways of life and many activities can fall under this end: work, service, play, worship, creation, learning, love. Fulfilling this purpose is also marked with trials and suffering; it is a difficult choice, and one that we must weigh against other forms of life. I also believe that it is one that allows us to live lives of personal authenticity. Weighty stuff for a kids' movie.
Note: Pixar's two other most recent films, WALL-E and Up, are also films of great spiritual significance.