To clarify the writeups given above,
Thaumaturgy is a "
discipline" -- really a form of blood magic -- developed by the newly-minted
vampires of
Clan Tremere around
1120 CE. You see,
Clan Tremere was originally
House Tremere, an organization of human
magi who belonged to a magical order known as the
Order of Hermes. The leaders of House Tremere turned themselves into vampires after their spells -- particularly those which prevented aging -- began to lose their efficacity. Believing that, as vampires, they would have all eternity to work out a solution to the problem of this fading of magic (which turned out not to be fading, but simply changing... undergoing a
paradigm shift).
Unfortunately, in the World of Darkness, if you are a practitioner of True Magick as Tremere and his followers were, and you turn yourself into a vampire or get Embraced, your Avatar is destroyed and you can't work True Magick any more. This was a problem for the Tremere, since they needed magic both to prevent the Order of Hermes from realizing that they had turned themselves into massasa, and to fight off the other clans of vampire, most notably the Tzimisce, Nosferatu and Gangrel, since these were the vampires that the Tremere used to effect their transformation.
The Tremere solved this problem by developing paths of thaumaturgy, vampiric blood magic, which were based on their particular style of Hermetic True Magick. With the help of a little-known path of thaumaturgy called Rego Magica, they were able to convert Hermetic spells into thaumaturgical paths and rituals quite quickly.
The Tremere succeeded in their battle for survival, and thanks to their magical powers have become the most powerful -- and the most feared, hated and distrusted -- clan in the sect known as the Camarilla. They frequently barter their services for favors, but they never, ever teach their Art to outsiders. It is only thanks to their monopoly that they have survived this long, and they aren't about to give that monopoly up.
It is believed that other vampire clans have invented and practiced forms of blood magic -- the Followers of Set and the Assamites in particular -- but their knowledge is rare in the extreme. The Tzimisce art of Koldunic Sorcery is somewhat more common, but still unusual. Tremere Thaumaturgy is the only truly ubiquitous -- and arguably the most versatile -- of the vampiric magical arts.
One point that must be made clear is that Thaumaturgy is very different from normal vampiric disciplines. Thaumaturgy is divided into "paths", each of which contains five spells or "levels" which can be used instantaneously, without preparation or overt action. There are a potentially unlimited number of thaumaturgy paths, and any vampire with skill in thaumaturgy can learn a new path; the same is not true for an ordinary vampiric discipline. Then there are thaumaturgical rituals, which can have powerful effects but require significant amounts of preparation (and can last for days). Rituals go up to level 10; paths only go up to level 5.
I should mention that all this is quite fictional; it relates to the World of Darkness role-playing games such as Vampire: The Masquerade, published by White Wolf Game Studios. I would also like to say to Threed, as an avid Tremere player -- those are fightin' words. Now, where's that Certámen circle...