What is a Keyblade Master indeed.
In Kingdom Hearts, Sora is deemed the Keyblade Master by various folks. However its possible that due to the lack of knowledge on the Keyblade, purpose, and its origin, allowed for such an assumption. "There can't be two Keyblade Masters" said Riku. Riku obtains knowledge of the Keyblade from Malificent. Malificent either misled Riku into thinking that he was a Keyblade Master or did not care for the trappings of Keyblade titles.
So far, we know of several instances of how the Keyblade can be activated.
Being Chosen: When a strong hearted individual capable of wielding the Keyblade, is chosen by the Keyblade. In this instance, the wielder is considered to be the rightful owner of the Keyblade. However, under certain circumstances, the Keyblade may choose someone else.
A Seeker: When a strong hearted individual ventures out and locates the Keyblade his or her self by crossing over to other worlds and pinpoint its location. The Keyblade does not choose the individual, the individual recovers the Keyblade, and if the idnivdual's heart is strong enouogh, he or she is able to wield the Keyblade.
A Giver: When someone of higher status gives someone else possessing a strong heart, a Keyblade. He or she may not have been the rightful owner, seeker, or discoverer of the Keyblade, but the individual is still able to wield it because he or she, has a strong heart capable of wielding the Keyblade.
A creator: When the six princesses of heart were captured, they're power was used to create the Heart Unlocker (unofficial name), a Keyblade capable of opening the hearts of individuals, releasing darkness hidden away. Not sure if the Keyblade can be used to release light of the individual's heart. This is the only time as far as we know, that the Keyblade can be created.
A Stealer: When someone of a strong heart takes away the Keyblade belonging to another individual, making the Keyblade his or hers.
An awakener: When the Keyblade is awakened by the power of the individual's heart. In this since, the wielder is the only owner of this weapon. However the Keyblade can be given to the another individual for a specific amount of time, but this weapon is exclusively tied to its owner.
Now that we know the instances in which an individual is able to wield a Keyblade. How do we determine what a Master is?
We know the Keyblade's Ultimate purpose is to lock or unlock the heart of worlds. But what else is it used for? Releasing a captive heart maybe, as it could release the heart which is held captive by the heartless. Surely it could apply to natural human beings. That is what I think the other purpose is.
Keyblade Masters have a direct place in the Kingdom Hearts Universe. The spirit and will of the Masters, are that of their students. They must teach their students proper usage of the Keyblade. I made a thread about what a Keyblade Master and wielder's purpose is a good while ago. I believe they have a connection to Kingdom Hearts. More like they pass the hearts along and or keep order of the world. The students just learn their masters' ways, so that they could take up their oath as Masters one day. The dissapearance of Master Xehanort and his apprentice, hints toward something negative.
Of course that last bit was speculation, but oh well.