The Deathly Hallows: What the Three Objects Really Mean
The tale itself
The Tale of the Three Brothers is a fairy tale within the wizarding world about three brothers who meet Death. Each receives a gift: the eldest gets an unbeatable wand, the second gets a stone that can summon the dead, and the youngest gets a cloak that makes the wearer invisible.
The eldest brother is killed for the wand. The second brother uses the stone to bring back the woman he loved, but she's a shade, not truly alive, and he kills himself to join her. The youngest brother lives a long life, hidden under the cloak, and greets Death as an old friend.
The fairy tale is a parable about the right way to face death. The first two brothers try to conquer it or reverse it, and both fail. The youngest brother accepts it, and lives well because of that acceptance.
What they mean for Harry
Harry possesses all three Hallows by the end of book seven. He inherits the cloak from his father, receives the stone from Dumbledore, and wins the wand through a chain of allegiance that runs through Draco Malfoy.
But the point of the story is that Harry doesn't use them the way the brothers did. He doesn't seek the wand for power; he wins it by accident. He uses the stone not to bring back the dead but to ask for courage as he walks toward his own death. And the cloak has been with him since he was eleven, keeping him safe without making him reckless.
The Hallows are a test, and the person who deserves to master Death is the one who doesn't try to. Harry walks into the forest to die, and that willingness is what brings him back. It's the same logic as his mother's sacrifice: love freely given is stronger than any weapon.