How does the Resurrection Stone help attain mastery of Death?

Question

I kinda get the Wand and the Cloak, but I don't get the Stone.

If the possessor is supposed to be Master of Death, if someone were to kill the possessor, the Stone would still not be able to resurrect them, even with help from someone.

How exactly does the Resurrection Stone work then?

Answer 1

The Stone doesn't bring back the dead, and "Master Of Death" is just a title, not literal.

The Stone

Firstly, the Resurrection Stone doesn't bring back the dead. Rowling has gone on record as stating that magic cannot bring people back from the dead.

...one of the most important things I - I decided was that magic cannot bring dead people back to life; that' - that's one of the most profound things, the - the natural law of - of - of death applies to wizards as it applies to Muggles and there is no returning once you're properly dead, you know, they might be able to save very close-to-death people better than we can, by magic - that they - that they have certain knowledge we don't, but once you're dead, you're dead. So - erm - yeah, I'm afraid there will be no coming back fro- for Harry's parents

The Stone conjures apparitions that very much appear to be the "ghosts" of the dead however, so what gives? Look at how they are described.

They were neither ghost nor truly flesh, he could see that. They resembled most closely the Riddle that had escaped from the diary so long ago, and he had been memory made nearly solid. less substantial than living bodies, but much more than ghosts, they moved toward him, and on each face, there was the same loving smile.

Well, we know of at least one other instance that produces similar shadows - Priori Incantatum.

...though the thick gray ghost of Cedric Diggory (was it a ghost? It looked so solid) emerged in its entirety from the end of Voldemort's wand...

Dumbledore later explains this effect.

"No spell can reawaken the dead," said Dumbledore heavily, "All that would have happened is a kind of reverse echo. A shadow of the living Cedric would have emerged from the wand... am I correct, Harry?"

"He spoke to me," Harry said. He was suddenly shaking again. "The... the ghost of Cedric, or whatever he was, spoke."

"An echo," said Dumbledore, "which retained Cedric's appearance and character..."

It seems likely that one of the Perverall brothers succeeded in recreating the effect of Priori Incantatum, and bound it to the stone.

Master Of Death

Basically nothing about the afterlife side of the legend of the Hallows is true - it's all stories and metaphors that sprung up around several powerful wizarding artifacts created by three brothers. Dumbledore states this, and as we know, his guesses are usually right.

“—were the three brothers of the tale,” said Dumbledore, nodding. “Oh yes, I think so. Whether they met Death on a lonely road . . . I think it more likely that the Peverell brothers were simply gifted, dangerous wizards who succeeded in creating those powerful objects. The story of them being Death’s own Hallows seems to me the sort of legend that might have sprung up around such creations

The title "Master Of Death" simply means that the user has the ability to kill (the wand), to hide from death* (the cloak) and to not forget the dead (the stone). All sides of death are mastered, hence "Master of Death".

*Note, this means hide from danger, not hide from Death, the non-existent character from the story.

Answer 2

They don't

The phrase "Master of Death" does not mean what you think it means; though, in fairness, it doesn't mean what most of the characters in the book think it means¹.

The Hallows will not make you invulnerable, or even immortal. Rather, they show you that death is inevitable, basically by being the least-helpful possible versions of the things they claim to be. This gets pointed out in exhaustive detail in Dumbledore's notes on the Tale in The Tales of Beedle the Bard:

The moral of 'The Tale of the Three Brothers' could not be any clearer: human efforts to evade or overcome death are always doomed to disappointment.

^{The Tales of Beedle the Bard Chapter 5: "The Tale of the Three Brothers" Professor Dumbledore's Notes}

1. The Elder Wand is an admittedly super-powerful wand that, because of its reputation, makes the bearer a target for constant challengers (and death):

   What must strike any intelligent witch of wizard on studying the so-called history of the Elder Wand is that every man who claims to have owned it has insisted that it is 'unbeatable', when the known facts of its passage through many owners' hands demonstrates that not only has it been beaten hundreds of times, but that it also attracts trouble as Grumble the Grumbly Goat attracted flies.

   ^{The Tales of Beedle the Bard Chapter 5: "The Tale of the Three Brothers" Professor Dumbledore's Notes}

2. The Resurrection Stone teases (and tortures) the bearer with the false hope of reviving the dead, when it actually cannot:

   Beedle's story is quite explicit about the fact that the second brother's lost love has not really returned from the dead. She has been sent by Death to lure the second brother into Death's clutches, and it therefore cold, remote, tantalizingly both present and absent.

   ^{The Tales of Beedle the Bard Chapter 5: "The Tale of the Three Brothers" Professor Dumbledore's Notes}

3. The Invisibility Cloak is admittedly harder to fit into this metaphor, because it's not directly harmful, in the way the other two are. However, although you could theoretically use the Cloak to evade death by murder or manslaughter, it would be an awfully lonely life: by Half-Blood Prince, the Cloak barely covers three mostly-full-grown people, so it's doubtful you could fit more than two adults under the thing:

   "Our feet'll be seen!" said Hermione anxiously, as the cloak flapped a little around their ankles; it was much more difficult hiding all three of them under the cloak nowadays.

   ^{Harry Potter and the Half-Blood Prince Chapter 6: "Draco's Detour"}

   However, Dumbledore hints in Deathly Hallows that the Cloak may not work for everyone:

   [T]he Cloak, I took out of vain curiousity, and so it could never have worked for me as it works for you, its true owner.

   ^{Deathly Hallows Chapter 35: "King's Cross"}

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¹ To be totally fair, as you can see in my discussion with DavidS in comments, the idea of uniting the Hallows to become "master of Death" doesn't actually appear in the original myth at all; there's little-to-no evidence that uniting the Hallows has any real effect at all

Answer 3

The legend was that uniting all three made one "Master of Death". It was, in other words, trying to outsmart Death. For example, the two older brothers chose items that would 'humiliate' Death, not realizing in their arrogance that they were playing right into his hands. Only the 3rd brother asked for a gift that showed wisdom, seeking to evade Death, but the request showed reverence, even respect, in that only Death's own cloak could work against Death himself.

An individual who owned or won the gifts, but, did not lose to them could essentially be considered a Master of Death.

The Wand: Harry won the wand and used it to defeat Voldemort - but, he didn't want it. He used it to repair the phoenix wand. Therefore, Harry was master over the Elder wand as it did not hold him sway. He gave it back.

The Cloak: Belongs to Harry as it belonged to his father before him. Harry inherited the Cloak, therefore is its master.

The Stone: The real proof of Harry's mastery of Death lay here. Harry took the stone and used it not to bring others back from the dead, but, to have them give him the courage to face his own death. Dumbledore insisted that Harry didn't realize how special he was because he could love. Harry, in this very instance, shows the greatest possible love by laying down his own life. This is how Harry masters the stone, because he uses it to give him the strength to allow Voldemort to slay him, thereby breaking the curse and proving the prophecy. Because Harry used the stone to willingly face Death - the very thing that Voldemort feared - Harry proves that he is Master of Death. Additional proof is that Harry did not keep the stone either. He discarded it in the forest after his loved ones escorted him to his destination.