While it wasn't the world's first vibrator (an honor that belongs to a 1734 wind-up model called the Tremoussoir), George Taylor's "Manipulator", invented in 1869, was the first steam-powered vibrator.
It was common knowledge that females were weaker than men and inherently defective, medically speaking, and that their sickliness was directly attributable to their reproductive system, as a condition called "hysteria". The symptoms of hysteria included pretty much everything: nervousness, insomnia, too much vaginal lubrication, not enough vaginal lubrication...
According to the anatomist Galen, the cause of hysteria was the retention of "female semen", which could rot and corrupt the blood. Galen came up with a solution: female semen is released with orgasm, so if the woman is brought to orgasm - "twitchings accompanied at the same time by pain and pleasure" or, in Victorian parlance, "hysterical paroxysms" - hysteria can be treated and prevented.
The prescription for married women was simply: have more sex. But what about widows, and virginal young girls? Obviously they would have to be brought to hysterical paroxysm, and so the doctor would massage their genitalia until this occurred. Of note is the notion that if the woman wasn't being penetrated, it wasn't really sexual, so that it was entirely appropriate for a doctor to massage a girl's clitoris. Eventually, however, the doctors' fingers got tired. Hence the steam-powered vibrator.
The Manipulator took the form of a large table, from which protruded a ball that was connected to a drive train powered by a steam engine in an adjacent room. It (and other machines meant for the stimulation of female genitals(*), such as the "pelvic douche" that used a powerful jet of water) was mainly purchased by physicians and spas.
Other milestones in vibrator history include the first vibrator ever, a wind-up model (1734), the first electromechanical vibrator (1883), and the first battery-powered vibrator (1899).
(*) but NOT for pleasure, or fun. Nuh-uh. No way. This is medicine here.
References and further reading:
http://www.socio.demon.co.uk/magazine/5/5orgasm.html
http://www.salon.com/urge/feature/1999/02/cov_25feature2.html
http://www-rohan.sdsu.edu/~delmare/
http://www.loxosceles.org/archives/2003-01.shtml#2003-01-12
http://www.sexualrecords.com/WSRartifacts.html
http://www.libidomag.com/nakedbrunch/maines.html
Bullough, Vern L. Sex, Society, and History. Science History Publications, New York, 1976.