Boiling it down to the basics, here follows the way I would summarize the Christian thematic of the Harry Potter series. In this case, I'm not offering specific examples or any particular details, because each and all of those would lead in turn to further nuances and tangents and the sort of ongoing conversation that is great fun but potentially distracting from the point at hand.
I don't suppose that J.K. Rowling would put it the same way that I do here. The way that she has expressed herself is by writing the books in question! And as I've said before, I don't believe that she set out to write a kind of propaganda for Christianity. I take her at her word, though, that she is a Christian, and I find it rather clear and obvious that her Christian faith in Christ, His Cross and Resurrection, informs the underlying theme and contributes significantly to the contours of the story. Of course, there were all sorts of other influences upon her, both literary and historical, as well as her life experiences and larger world view (of which her faith is a significant component). In more ways than one, she follows in the vein of C.S. Lewis and J.R.R. Tolkien, whom she has cited among her foremost literary influences. All of these factors were brought to bear upon her writing of this epic fictional creation, which she first imagined and began to write in the final months of her mother's life. I am convinced that coping with her mother's death from Multiple Sclerosis in those early days, as Rowling was working on the first book in the series, shaped a good deal of her thinking and progress throughout the entire work.
So, anyway, here is how I summarize the theological significance of the Harry Potter books in my own words:
The fundamental question taken up by the books is this: How does one face and deal with death? The answer: In the faith and hope of the resurrection and the life everlasting.
Fear of death leads to a lust for power, to a desperate striving for self-preservation at all costs, and so to hatred and envy and disregard for others. Ironically, the consequence of this fearful quest to avoid death is a soulless (loveless) existence, which is a kind of living death (an ongoing, self-perpetuating fate worse than death).
Those who live by faith in the resurrection, live in love for others. They are willing to sacrifice themselves for the sake of what is good and right, for others. They show mercy and forgiveness, even toward their mortal enemies. Dying, yet they live.
Such self-sacrificing love does not come naturally or easily, but by the traditio of catechesis and with the support of family and friends. Life under the Cross is an ongoing battle, full of demonic temptations to doubt and despair, on the one hand, and to a selfish, self-centered, self-justifying self-preservation on the other hand. In the midst of this warfare, faith and life are sustained by the community of love, and the Christian disciple cries out in expectant hope for the help that comes from the Father. But progress is not steadily and continuously upward. It is, rather, a process of dying and rising, and of being served and rescued by the servants of Christ Jesus. In other words, it is a daily and lifelong return to the significance of Holy Baptism, that is, the Cross and Resurrection. In this, the Christian draws strength and encouragement from the example of the martyrs, who direct his eyes unto Jesus Himself, the Author and Perfecter of faith.
Although the self-sacrificing love of Christ Jesus and His disciples appears weak and futile, it is the strongest "magic" of all, which prevails over hatred and death, and gives life to others. In this faith and love, one approaches death and faces it with courage and quiet confidence.