To be killed permanently and absolutely, the entirety of a person's soul must be destroyed. When part of it lies hidden in a Horcrux, it is impossible to kill the witch or wizard without first destroying all the Horcruxes they created. Obviously, this is of immeasurable importance to those dark wizards seeking immortality, particularly if the locations of the Horcruxes they made are hidden.
Most significant, though, is Voldemort's use of Horcruxes. It explicitly explains why he wasn't killed when the Avada Kedavra curse intended for Harry rebounded and hit Voldemort instead. As Hagrid put it, "Dunno if he had enough human left in him to die."
Dumbledore said he believed Voldemort made six Horcruxes, with the original part of his soul still remaining in his body. The locations were:
The Gaunt Ring (DESTROYED)
Riddle's Diary (DESTROYED)
Nagini, the snake
Slytherin's Locket, stolen by R.A.B (which some have speculated is the locket that wouldn't open from the glass cabinet in Book Five)
Helga Hufflepuff's Cup
An item of Rowena Ravenclaw's or an item of Godric Gryffindor's.
The first five seem perfectly legitimate, but the last two possibilities have been the subject of heated debate. Since the beginning, Rowena Ravenclaw has been described as wise and shrewd, suggesting she wouldn't allow an object of hers to be used for such evil. Furthermore, Godric Gryffindor's sword and the Sorting Hat currently reside in Dumbledore's office, and since he told Harry only a Gryffindor could pull the sword out of the hat, it seems unlikely Voldemort would have been able to make it into a Horcrux.
Thus, speculation is rife about the location of the last remaining Horcrux. Some possible locations:
Riddle's Award for Services to the school (Riddle liked to collect "trophies", which we assumed was a metaphor...but Jo might have meant for us to take it literally!)
The sinister box from the glass cabinet in Book 5
Harry Potter himself (Dumbledore keeps saying Voldemort left some of himself in Harry the night he tried to kill him, perhaps this is part of his soul!)
The last one is particularly interesting. Voldemort couldn't have created a Horcrux from Harry because he didn't kill him, but he could have made Harry into a Horcrux from killing Lily or James (accidentally we must assume, as he wouldn't have created a Horcrux only to try and kill it). If Harry is indeed the last Horcrux, this means that for Voldemort to die, Harry must die. This could work in two ways:
Harry destroys all the Horcruxes except himself, then kills himself and Voldemort at the same time.
Harry kills all the Horcruxes, including himself, leaving Voldemort completely mortal so that someone else can kill him.
Naturally, this is a horrible thought, but we must consider the possibility that Harry will have to die!
Post Deathly Hallows Analysis
For the most part, our speculations about the final Horcruxes were correct. An item of Rowena Ravenclaw's was indeed a Horcrux and it was the tiara first seen in the Room of Requirement in Half-Blood Prince. Also, we deduced the sword of Godric Gryffindor was not made into a Horcrux. It instead turned out to be a destroyer of them.
And of course, we were right in guessing Harry Potter himself was a Horcrux. This concept, in particular, sparked many a heated discussion; and they often yielded the most depressing conclusions. And so, for the many of us, we accepted Harry's death before ever even turning the first page of Deathly Hallows.
And he did die in some capacity, didn't he? For a little while, anyway. To our delight, Harry survived virtually unscathed after being hit by the Avada Kedavra once again. And his spirit returned purified of Voldemort's dirtied soul after being sent to a place like Christian purgatory and Dumbledore.
Culminating in the final events of Deathly Hallows, this books series that we know and love fully unraveled itself to us at the last installment, and revealed its truest tension, which turned out to be the greatest most devastating truth that every human being eventually faces: we are all going to die someday. The Harry Potter books are concerned with Man's mortality in mind - the very first book begins with the death of Harry's parents and the subsequent wild revelation of Voldemort's believed death sends wizards out into the streets.
As such, Jo has constantly brought us characters who have become characterized by their obsession with "beating" death. As early as book one, we were introduced to Nicholas Flamel, his philosopher's stone and elixir of life, which could keep a man alive forever as long as he continues to drink the potion. In Half-Blood Prince we learned about Voldemort's Horcruxes, items which - if preserved from destruction - could preserve a person's spirit on Earth even after the destruction of their body. And finally, in the last book, we discovered the truth about Dumbledore's obsession with the Deathly Hallows, which, if assembled together, are said to bring the user a mastery over death. Thus, surpassing (or perhaps controlling) death is a prevalent theme in the Harry Potter series - and therein lies the significance of creating Horcruxes, arguably; the most selfish method of immortality among the ones here described.
It is a selfish method because, in order to create a Horcrux, you must commit a murder. Your survival is completely dependent on your ability to take another life. (A skill that Voldemort prides himself on: he makes eight Horcruxes.)
Then who, if anyone, could possibly be termed a master of death, when their very drive for mastery of it is inevitably linked to their fear of it, of the unknown, of darkness, and of non-existence?
As we first started reading, the master of death seemed to be a one who possessed all three Deathly Hallows: a person who was 1) unbeatable with the elder wand, 2) invisible from Death himself with the magic cloak, and 3) able to recall departed spirits into being with the resurrection stone. In possessing all three of these powers, surely a wizard could name himself a master, fully protected in every respect from the woes of death - but Dumbledore, repenting, offered a different answer:
"The true master does not seek to run away from Death. He accepts that he must die and understands there are far, far worse things in the living world than dying." Dumbledore page 720, DH
Even the greatest witches/wizards/people have times in their life where they struggle with their own demise. But as Dumbledore has made quite plain, the story of the master of death refers to a specific kind of bravery - not cowardice. To face destruction openly as the final ending, and then to move on and love yourself, your family and your friends anyway, that is to be the real master.
This is why Harry Potter is our hero. Not because he's a particularly powerful wizard, not because he had a hand in slaying Lord Voldemort, but because he's an exceptional human being. By no means is he perfect, (though perhaps we'd like to think so!), but he successfully became a master of death when Dumbledore could not - saw the needs of his loved ones as greater than his own desires. To create a Horcrux is to do the exact opposite; and, in a larger sense, the conflict between Harry and Voldemort reflects very real life philosophies, which have been in opposition in our society since its' beginning and remain in common discourse today.
It all boils down to this: does the life we lead really matter if we're going to die in the end? According to JK Rowling, that is precisely why it does.