Baphomet is a symbol used by various esoteric groups.
The origin of the term "Baphomet" is not fully understood. It is likely a combination of the Greek words baphe and metis, meaning "absorption of knowledge."
Original depictions of Baphomet are associated with the Knights Templar. He was represented as a human skull, or sometimes a black cat, and presided over the domains of wealth and fertility. (It is important to note, however, that many accounts of alleged idol worship performed by the Knights Templar were greatly exaggerated by their accusers.)
By far the most recognizable depiction of Baphomet was drawn in the 19th Century by French occultist Elpihas Levi. (http://25.media.tumblr.com/9df52611a4faae7f5234ea06e8367cbb/tumblr_mftoqtagQa1s15gnco1_1280.jpg) In it, Baphomet - here called 'the Baphomet of Mendes' - is represented as a hermaphrodite half-goat with a cadeuces as a phallic symbol, a torch between his horns, a pentagram on his forehead, and the Latin words SOLVE (separate) and COAGULA (join together) are emblazoned on his arms. Above him is a waning crescent against the night sky; below him is an eclipse.
This depiction of Baphomet was later used by Aleister Crowley. In narratively-written magick rite, The Gnostic Mass, he alludes to the deity in a line uttered by the congregation: "And I believe in the Serpent and the Lion, Mystery of Mystery, in His name BAPHOMET."
Baphomet was a potent fertility symbol; Crowley postulated that Baphomet, as a divine andogyne, represented the union of the sperm and the egg - the masculine and feminine - at the moment of conception, and the "magical child" that resulted from unions born of sex magic. Crowley also believed Baphomet to be "the heiroglyph of arcane perfection."
Below this line, I have written my own personal experiences and speculation relating to Baphomet. He is not an officially canonized deity in any other spirituality except Thelema, pioneered by - you guessed it - Aleister Crowley. My personal meditations have revealed him to me as a patron deity, and I am curious to know if anyone else's firsthand accounts were similar.
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It's difficult to list off the domains Baphomet presides over due to his dualistic nature. He is both a fundamentally sexual character, but is asexual; he represents the totality of knowledge, as well as its utter lack; he represents magic intuition and access to the higher plane, as well as bodily preoccupations that keep us grounded to the physical. Baphomet is a complex and poorly understood deity whose workings, though they appear random and amoral to us, do have a methodology.
Baphomet's workings are cerebral and cosmically oriented. He is unconcerned with the petty workings of humans, having long since seen beyond their scope to the needs of every particle of matter, living and non-living, that resides within the observable universe. He often manifests in the form of ironies, coincidences and deja vus that are profound, strange, and deeply significant.
My personal experiences with him as a patron deity have yielded mostly nonsense, and I say that in the nicest possible way. Baphomet is far removed from the experience of humans, and has difficulty speaking to them in words, expressions, and sometimes even languages they understand. He prefers to convey his message through abstract and impressionistic ways that may take some thought to fully comprehend.
I've found he has a fondness for myrhh, onycha and mandrake root. His colors are purple, blue, silver and black, and his favorite days are Saturday and Monday, particularly if they fall on a night of the new moon.
Though he is ambivalent to my needs and wants, as he is with all other creatures, he gifts those who pay him homage or leave him offerings with increased incidences of "weirdness" in their lives - coincidences, deja vu, lucid dreams and improbable outcomes to events. His influence brings strangeness and intrigue.