"Keyblades are said to be man-made counterparts to Kingdom Hearts. The χ-blade, however, coexists with Kingdom Hearts."
"Using the X-blade as a model, [The Master of Masters] creates his own Keyblades. Well, by create I don’t mean that in the physical sense, such as forging and tempering them, I mean more along the lines of pulling one out from the depths of a heart."
"There are as many Keyblades in existence as there are hearts qualified to wield them. At this stage, the only requirement that has been made clear is that someone must have a "strong heart", but there are other requirements that haven't been spelled out yet which I plan to reveal another time when I have the chance."
"To use a keyblade you must have been chosen to inherit as well as been chosen by the keyblade itself. In BbS you could see that Terra performed the ceremony with Riku, and that is why Riku was able to take the keyblade that Sora used. The keyblade inheritance ceremony is performed with a keyblade master touching someone using a keyblade."
Yuffie: The Keyblade chooses its master. And it chose you.
---Does not the Keyblade itself choose its owner?
Nomura: The Keyblade reacts to the rightful owner’s heart and appears to them.
Terra (reciting): In your hand, take this blade. And so long as you have the makings, then through this simple act of taking, its wielder you shall one day be made.
Through careful phrasing, Nomura has created two seemingly opposing truths for KH lore. One truth is that keyblades are the man made replicas of the X-Blade. Another truth is that the keyblades have a will of their own, and that they choose a master. The following is the whole truth; the Keyblade Inheritance Ceremony allows keyblades to choose hearts in which a keyblade may be forged.
Let's go back to the beginning, The Master of Masters presumably obtained the X-Blade and studied it. After some time, he managed to reverse-engineer the thing and created the very first man-made replica of the X-Blade, a keyblade known as "No Name". After he created this keyblade, he was later able to pull keyblades from the hearts of the Foretellers, but how? He performed the Keyblade Inheritance Ceremony on them of course, but what exactly is that? What does it do?
I present to you the Dandelion Theory which explains the Keyblade Inheritance Ceremony. Using the dandelion as an analogy, we can see distinct stages in the life cycle of a keyblade (refer to the illustration above). First we have a worthy heart as noted by the crown (top), I believe that the crown symbolizes a "kingdom quality" or a connection to Kingdom Hearts and all the crowns we see in this series carry that same symbolism. I'm unofficially using these symbols to my own ends as illustrations, but it should be noted that Aqua and Terra were able to recognize worthy hearts at a glance and even see (in Aqua's case) that a heart had already undergone the ceremony. Therefore, I believe that worthy hearts have a certain "kingdom quality" that can be observed by both keyblades and keyblade wielders alike.
The second, third, and fourth stages (right, bottom, and left respectively) are interconnected and thus hard to discuss individually. After a worthy heart undergoes the ceremony, a seed is planted within that heart. As time passes, the heart nourishes that seed and it eventually blossoms as a flower - the complete keyblade. However that keyblade has yet to mature, it has yet to show the Mark of Mastery. The Mark of Mastery is a keyblade fully matured, a flower that may spread seeds of its own. This is the Dandelion Theory, that the Master of Masters forged keyblades in such a way that they self-replicate. Seeds are interesting because they store the biological data of their forebearers. Thus the heart uses the data found within a seed as a sort of blueprint to create a keyblade of its own.
---
The theory itself ends there, but going a step further let's look at the implications here.
Spoiler Show
Sora obtained a keyblade without the ceremony and this was a simple matter of him stealing Riku's Keyblade (hereon Kingdom Key). It wasn't because of Ventus, and it certainly wasn't because Sora was so special that he didn't need the ceremony. Rather, when Sora (inadvertently) reached within Riku's heart, Kingdom Key responded seeing Sora as a more suitable wielder. The seed that had spend ten long years growing had bloomed and deemed its host unworthy. At more than one point in that same game the two keyblade wielders call forth Kingdom Key from each others hearts until it finally settles for Sora once and for all. Flash forward to Kingdom Hearts II and we have Riku calling forth Kairi's keyblade from her heart, a complete keyblade that she simply hadn't been able to summon by her own power yet. Speaking of KH2 however, Riku obtains his second (and replacement) keyblade - Way to Dawn. Nomura said "I would like you to think that something not fully explained, outside the usual method of acquirement, is going on here.", so what is it? He obtained another seed, and he obtained that seed from Xehanort.
Xehanort is a Keyblade Master with a seed bearing heart. His plan is to insert a fragment of his heart into multiple vessels so that the fragment will slowly consume the host's heart. His capacity to do this is directly proportional to the darkness within a heart, it is the darkness within a heart that gives him control. Once he obtains his desired number of vessels, thirteen darknesses, he plans to have them clash with seven lights and forge the X-Blade. There is often a misinterpretation here, the clash of seven and thirteen isn't the keyblade war - its what starts the thing. That being said, it wouldn't be a stretch of the imagination to believe that the seed bearing heart of Master Xehanort would give rise to new keyblades being forged within the hearts of his vessels.
Sensing the possibility, Yen Sid sought to ensure that Sora and Riku produce the Mark of Mastery in order to combat this threat. Perhaps Keyblade Masters are limited in how many seeds they can plant or more likely in how often these seeds can be planted. Thus with Sora and Riku as additional masters, they could add more legitimate keyblade wielders to their ranks (Roxas, Xion, etc). While Sora and Riku took their test, Lea came to Yen Sid and he performed the Inheritance Ceremony on the fiery red head. Merlin then sped up the process and by the end of the game Lea was able to summon his own keyblade.
At first it seemed a bit contrived to give Lea a keyblade, but it makes sense. Not everyone forms a nobody when their heart is lost to darkness, only those with strong hearts form nobodies. That's right, a strong heart produces a dusk - the lowest tier of nobody. Stronger hearts produce class-tier nobodies. It is only the exceptionally strong hearts that produce human-tier nobodies, and interestingly each of these human-tier nobodies bond with an element (almost as if it stabilizes them). What I'm suggesting here is that by the nature of producing human-tier nobodies, the potential to also have a kingdom quality heart is extremely high. This is also why Xehanort held a vested interest in filling Organization XIII with fragments of his heart.
Spoiler Show
The keyblade seems to possess a sort of quasi-sentience, I believe this stems from being deeply connected to a wielder's heart. After all, the heart can unintentionally grant sentience to elemental darkness in the form of a heartless. So it would make sense if the keyblade's will is in line with that of its creator (making Kingdom Key particularly interesting). Keyblades do not have hearts of their own however, they are more like an extension of their wielder's hearts. Keychains seem to be these metaphysical objects that not only change the physical form of the keyblade, but also function as a source of life if the Keyblade Graveyard is any indication, but that aspect is entirely unclear. Once a wielder dies, a keyblade also seemingly dies, but not always. Some keyblades like No Name and Master's Defender have somehow lived beyond their wielders. A keyblade separated from a wielder can usually be summoned back to a wielder, but not always (being in different realms seems to make this impossible). A separated keyblade in the hands of a wielder seems to be fully functional, but in the hands of non-wielders a keyblade seems little more than scrap metal. Keyblades also seem to weaponize the strength of a person's heart, perhaps explaining why they don't do much in the hands of non-wielders.
Spoiler Show
I don't believe that a strong heart is the only condition for becoming a wielder however. After all, Nomura said it himself...
Another requirement is clearly having the ceremony performed on a potential wielder, but Nomura mentions requirements plural, as in there are other things too. This circles back to the kingdom quality that I've mentioned multiple times now. I don't think it's just a strong heart, I think that a kingdom quality is something more than that. I honestly don't know what else to call this or what it could be.