The Master was an incredibly powerful vampire who was the leader in the Order of Aurelius, a group of select vampires who lived together in a sort of vampire society.
His order moved around the world for many centuries, probably based on where they could be the most safe and get the most food. Over this time, he would sire select people to become part of his order, and also recruit other vampires who were worthy.
In the late 1930s, his order came to Sunnydale with the purpose of opening the Hellmouth, and bringing hell to earth. However, in 1937, while trying to open The Hellmouth, an earthquake ruined the delicate ritual. It destroyed half the town, and the church The Master was performing the ritual in was buried underground... Not only this, but The Master was trapped in the dimensional portal, unable to leave a confined area in the church.
Sixty years later, a once in a century ritual was able to be performed which could free The Master. The ritual was called The Harvest and consisted of Luke becoming The Master's vessel. For one night, if Luke fed off enough people, he could transfer the power he gained to The Master, and free him. Unfortunately for The Master, Luke was killed when The Slayer discovered the plan. The Master stayed trapped as a result.
The next thing The Master did was have his vampires attack a bus and sire The Anointed One, who was to play a part of a future prophecy that was said would lead to the Slayer's death, and the Master's freedom. The Master treated The Anointed like a son, and taught him the rules of his vampire society.
When the prophecy was ready to take place. The Anointed lead The Slayer to The Master. The two fought for a short time, but The Master easily overcame the Slayer. He was able to bite her, drink a small amount of blood, and become free of his prison. He then pushed The Slayer into a pool of water where she drowned. What The Master didn't count on however, was CPR, which brought The Slayer back to life. She then killed The Master by pushing him through a skylight and onto a large piece of wood.
A few months later, The Anointed got together the few remaining members of The Master's order and attempted a ritual to use The Master's bones to resurrect him. The Slayer was able to stop him, and then smashed The Master's bones to prevent any further attempts.
The Master was one of my favorite vampires ever seen on the show. His exact age is unknown, but Giles said he's as old as any vampire on record. To me, this means that perhaps he even predates the records that the Watcher's Council has. His extreme age is seen in the way his face is deformed and he is unable to take human form. The only other vampire ever shown to be deformed has been Kakistos, who we know was at least around 2000 years old (because his name was from ancient Greece.) I suspect The Master to be older, and I think it's even possible that he was one of the first vampires from around the time where humans had just started to become the dominant species on earth.
The Master also had some limited kind of mind control powers. Buffy referred to it as hypnotism, if this is the case, he certainly is very good at it, he was able to make Buffy freeze in her tracks by simply reaching out toward her with his hand. It's possible that he learned this, much like Dracula learned some magic. It could also be something that he was gifted with as a human, like Dru's powers to see into the future. Or it could be natural to a vampire of his age, after all, it is certainly possible that vampires have limited powers like this that they use in siring, and as a vampire gets older, their powers get stronger. Perhaps The Master has developed the ability to the point he is able to use it in circumstances other then siring. It just personally makes more sense to me.
Another thing unique to The Master was the fact that when dusted, he left behind a skeleton, even other vampires who are old enough to deform (like Kakistos) have been shown to take their skeleton with them. Is it because The Master is simply older or is it because The Master was incredibly powerful? perhaps a bit of both. I really don't know, but I'll say age because that makes things less complicated.
The Order of Aurelius is fascinating. It had lots of rules that many modern vampires don't follow; Such as respecting the life of other vampires and living underground. I think that there are other similar orders still left in the vampire world, each with similar rules and it's own head vampire. Most will stay quiet and out of The Slayer's way and this is why we have never seen them, they are probably so low profile that The Watcher's Council might not even know some exist, and those they do know exist, are so well hidden and integrated they can't be hunted down. Most vampires we see on either show are ones out for themselves or are part of small gangs, not trying to be part of a larger vampire society. The Master clearly was, probably because he's been around since before humans had any real society. Even in the alternate universe (where The Master broke free on The Harvest and was not killed) he was shown and trying to promote vampires as a society.
Actually, there is some evidence of Watcher confusion regarding The Master's order. Giles referred to the Order of Aurelius as a small group of vampires who came to The Master to sire The Anointed One. When in actual fact, later episodes showed that The Master was the Order of Aurelius. Now, the real reason behind the show is probably a change in plans, sometimes in TV shows they’ll want to change the story. Still, for purposes of this site, there was no indication by The Master that he wasn't part of The Order, and so it can be said that Giles was simply wrong (actually, if you watch the earlier episodes, The Master does seem to refer to himself as part of the order on one occasion, and Buffy does seem to recall the order's symbol from somewhere before... almost makes you think it might have been planned all along…). I doubt that a vampire who lived so long would flash around his name and organization to mortals anyways now would he? It’s easy to understand why the Watcher’s Council wouldn’t know.
Another thing of confusion is the nature of The Master being stuck. In the first episode, The Master is shown rising from a pool of blood. Some people think this implies that he had been stuck down there in a sort of limbo state since the earthquake, and only can come out now because The Harvest is near. However, this is never said directly, and later episodes have The Master talking about how long he's been underground. I think it's most likely that The Master was always free to walk around in the confined space but he'd sometimes go into that pool of blood to regenerate, or meditate, or something of the like, perhaps for months or even years at a time. I also like the dramatic purposes of having him require feeding all the time being stuck down there, it just shows how loyal his Order would have been to stay with him.