Baphomet is a deity, demon and/or symbolic icon which originated in the 14th century as a supposed figure of worship of the Knights Templar. In those accounts, Baphomet was described as an inscribed head or human skull. The name "Baphomet" originally was a deformation of the name of Muhammad, the prophet of Islam. Claims that the Templars were worshipping "Baphomet" meant, in fact, that they were secret Muslims. Medieval European folklore did not recognize that Islam was a monotheistic faith, and imagined instead that Muslims prayed and sacrificed to a number of terrifying and evil imaginary deities.
In the 19th century, French occultist Eliphas Lévi formulated the modern conception of the figure via an illustration portraying it with wings, a horned goat's head and an emblazoned pentagram and breasts. The Freemasons were thereafter accused of worshipping it, after which it was incorporated into the theology of Thelema, and in turn into the iconography of LaVeyan Satanism.
Baphomet represents all opposites and equalities in the universe, similarly to the Yin and Yang. It's often portrayed as controlling the sun and moon, night and day, good and bad, up and down, and male and female. It has breasts to symbolize femininity and the caduceus of Hermes to symbolize masculinity.
Baphomet represents the perfect and ideal human. It embodies everything in the universe, not unlike God himself. The mastery of the spiritual and physical world represents complete religious enlightenment. The pentagram on Baphomet's forehead represents the ascent of matter into spirit; the four lowest points represent earth, fire, water, and air, while the top point represents soul. Thus, soul is above the physical world, a truly enlightened being. The inverted or upside-down pentagram, wrongly thought to be satanic, represents the descent of spirit into matter. Thus Baphomet completes the circle and is a being who both ascends into spirit and descends into matter. The words on his arms, Solve & Coagula, represent the alchemical and spiritual process of becoming an enlightened and liberated being.
In 1307, King Philip IV of France owed a lot of money to the Templars (and was furthermore angry at them because they wouldn’t let him become a member) and figured he could weasel out of it and take revenge on his creditors by slandering them into oblivion. On October 13, he ordered the arrest of hundreds within France on charges of all the usual suspects (heresy, apostasy, idolatry, devil worship, homosexual orgies, money laundering, etc.), and had them tortured until they confessed to anything he wanted to hear.
The worship of Baphomet was not, unto itself, one of the charges; however, a handful of the internees brought the name up on their own accord. It should be noted that the Templars' account of the figure offered at this point was different from that of the modern conception, described variously as: an idol with a human skull, a head with two faces, a cat idol or a bearded head. Whatever the case, the figure supposedly served a role in the Templars' initiation ceremonies.
The image that everyone envisions when they hear the name "Baphomet" - that of a winged humanoid goat with a pair of breasts and a torch on his head between his horns gesturing towards two crescent moons - did not appear until over 500 years after the business with the Templars. This image - also known as the "Goat of Mendes" - comes from Eliphas Lévi's 1854 Dogme et rituel de la haute magie (in English known as Transcendental Magic).
Lévi's depiction, for all its fame, is not particularly authentic to the historical description from the Templar trials, although it is not unlike gargoyles found on several Templar-built churches— or Viollet-le-Duc's vivid gargoyles added to Notre Dame de Paris about the same time as Lévi's illustration. Mainly, however, Lévi appears to have devised the figure by combining the depiction of the Devil in the Tarot de Marseille with the hieroglyphic depiction of the ram-headed Egyptian deity Banebdjedet, which was worshipped at Mendes but which Lévi mistakenly interpreted as goat-headed rather than ram-headed. In turn, Lévi's Baphomet image influenced the design of Devil cards in later Tarot decks made for the occult market.
Baphomet in Satanism
Another depiction of Baphomet that's almost as well-known as Lévi's drawing is that of the Sigil of Baphomet, wherein the horns, ears and chin of a goat form a pentagram surrounded by five Hebrew glyphs which spell the word: "Leviathan". This depiction originated in the book La Clef de la Magie Noire by French occultist Stanislas de Guaita, in 1897, and was later used in Mourice Bessy's book A Pictorial History of Magic and the Supernatural. In the 1960s, when Anton LaVey was formulating the Church of Satan, he decided to adopt this depiction as the symbol of his religion, in much the same manner that Crowley adopted Lévi's conception of the figure into Thelema. Once again, the figure, in this context, does not represent the Biblical Satan (whom LaVeyan Satanists do not worship in the first place), but rather simply comprises a metaphor for the Church's beliefs and values. The Church describes it as: "[The] preeminent visual distillation of the iconoclastic philosophy of Satanism."