Reincarnation is the great equalizer. By changing bodies and life situations, we are given countless chances to shift perspective. We have infinite opportunities to truly understand whatever it is we need to learn about the human condition from all possible points of view.
My favorite metaphor for picturing the purpose of reincarnation comes from Rabbi Omer-Man as he explains to the Dalai Lama the Jewish concept of rebirth (quoted in the wonderful book The Jew in the Lotus:
Each soul has to create a garment of light. In each incarnation... we make a little more or we undo a little according to our actions. In some incarnations, we do more damage, we pull out more threads; in other incarnations we weave more threads in. Ultimately the goal is to complete the garment.
As I see this image, when the garment of light is finally complete, we are light beings at one with God.