First, if you have not read the series or seen the films, *spoiler alert*. It has been awhile since both have come out, but I still say it because I truly believe these stories are worth it to be experienced. So please do not continue if you plan on reading the books. Read them and then come back.
Second, if you did read them and need a refresher course on the Deathly Hallows, here is the Tale of the Three Brothers to refresh your memory.
So let's get to it:
The Deathly Hallows is my favorite book in the series. It is not conventional to the other books, as the flow from the previous books is now thrown into chaos and open warfare. So in the book, Harry is made aware of the Deathly Hallows. From the tale, we discover that there are three parts to the Deathly Hallows being as follows: The Elder Wand, The Resurrection Stone, and the Invisibility Cloak. The three magical objects were given to the brothers by Death. They come from an otherworldly source, not simply from the hands of man. Each of these contain an aspect that, in my view, are a part of man's ultimate desire to attain perfection. When seperated and merely focusing on one aspect of them leads to a distortion of the whole, and likely to one's downfall (as the the death of the first two brothers display). Yet, the attainment of the 3 Deathly Hallows (DH), along with the possession of heavenly virtue, represents the perfected (Heavenly) man.
I want to talk about what each of the Hallows represents from a theological standpoint before I reflect more on the Hallows united as a whole.
The second DH given to the second brother is the Resurrection Stone given to Cadmus Peverell. A side note here, if anybody has watched the anime Fullmetal Alchemist would know about the Elric brothers in their pursuit of the Philosophers (or the Resurrection) Stone, the journey of bringing back the dead is a painful one. It need not be that way with Christ. Christ is the all-powerful King of the Universe who can do all things. Yet, one must follow the law and path set by God. Cadmus asks Death for the ability to bring back his deceased love, to which Death gives him the stone. Cadmus tries to take power into his own hands, but does not posses the strength or ultimate ability to perform such a miracle. The stone indeed is a sign of our return from the dead in a resurrected state. This is a big sign of the coming Kingdom of Jesus Christ.
The final DH, and a bit of unique request is Ignotus Peverell requesting the ability to hide from the world, including Death. The depth of this choice symbolizes that Ignotus is wise, and forsees Death's plan. He is given a supernatural item that can cloak him from all. With this wisdom and hiden-ness, Ignotus represents the rest of our family in the Church, namely the Saints. While Ignotus' brothers were using their magical objects for selfish purposes, Ignotus was living a life of learning and wisdom. I am sure he felt remorse for his fallen brothers and had hoped for their good fortune. He goes on to have a family, to which he raises a son and leaves the cloak to the boy when Ignotus greets Death "as an old friend, and went with him gladly, and, equals, they departed this life". That line also very much represents the rest of the Church as the saintly martyrs welcomed their death as a holy sacrifice to God, giving Him all the glory. They indeed welcomed Death as a friend as it was that veil they would pass through to greet their Lord and Master.
All Hallows... get it?
With the three we can see the symbolism of power, otherworldly life, and the wisdom of the saints. The final book in the series has Harry encounter each of the Hallows on his journey to defeat Voldemort. When in possession of all three, Harry does not use them for personal gain. He uses them wisely, and with a sense of virtue and heroism. Also, one thing of note, it was Dumbledore that possessed all three of the Hallows, keeping them safe until the time came for Harry to receive them. Dumbledore is the saintly figure who preserves the knowledge and items that Harry relies on to defeat evil, and this is much like our Christian journey. We await the coming of our Lord in power and glory, we await our resurrection, and we rely on the prayers and wisdom of the rest of the Church in Heaven (namely the Saints) to intercede for us to help us overcome evil.