
The Baphomet is so named after a demon considered synonymous with the Devil. He was recgonized by the Knights Templars as such.
The star surrounded by the bold ring is the Pythagorean star. The Temple of Set uses the Pythagorean Star as their official symbol, while the Baphomet is the symbol representing the Church of Satan and Modern Satanism in general.
Many people believe the goat's head found within the star is an image of the Devil. In truth, it is Pan, whose pre-Christian image was demonized. Pan, as stated before on this webpage, is the equivalent to Satan and symbolizes virility, sexuality, sensuality, and power.
The letters surrounding the boldened ring are Hebrew. They spell "LEVTN", or "Leviathan", another pre-Christian image. Leviathan was recognized by the Hebrews as symbolic of true wisdom.
The Baphomet sigil originated with the Knights Templars. During the Crusades, the Templars were the "Defenders of the Faith"--they were responsible for protection of the Holy Roman Crown during the times of the Turk invasions, and also were responsible for Christian invasions of elsewhere. After the end of the Crusades, the Templars outlived thier usefulness. Accordingly, the French and English kings systematically murdered the individual members of the Order and stole thier possessions. The gold and all other valuable metals were then used to fill the waning coffers of the Christian Empire.
The two points that branch out from the top represent Chaos (here, the aspect of duality) stemming from a One (the representation that the opposite perspectives of good and evil arise from the single view of the world). The other three points that move in conflicting directions symbolize denial of the holy, of essence (structures that apply a definition of the individual, attempting to apply a universally valid definition that restricts the role of the individual free will), and of classical philosophy (Objectivism).

Eliphas Levy was the creator of the Sabbatical Goat. Like the upward points on the Baphomet, the Sabbatical Goat represents duality.
The Goat has female breasts and a phallus in it's lap, representing the duality of the philosophic "masculine" and "feminine". The duality of these two forces are also represented by the goat's arms--one is a man's, the other, a woman's.
Each arm points in an opposite direction, one toward a dark crescent moon and the other toward a black one. This represents duality of "Good" and "Evil" (more about these dual opposites later).
Often, people will get confused by what appears to be a Pentacle on the Goat's forehead. In this case, it's not actually a Pentacle.
Neopagans (read: Wiccans) often claim that their Pentacle is the only true pentagram. This is not true. Their "Pentacle" is actually the "AR", also called the "Plough Sign". It originated in Mesopotamia and appears in the Sumerian religion. The AR represents the human race (in the Sumerian's case, it was specifically the Aryan race, but over time it has become inclusive of all races).
A "Pentacle" is only a Pentacle if it is used within the context of Modern Witchcraft (or Wicca). According to the Wiccan belief, the five elements are represented by the Pentacle: Earth, Air (or Spirit), Wind, Fire, and Water. Consequently, the elements are represented by the "Princes of Hell" in Satanism: Satan is the Element of Fire, Lucifer is the Element of Spirit/Air, Belial is the Element of Earth, and Leviathan is the Element of Water.
The Book of Revelation from the Christian Bible is obviously where this famous number originated.
Since the words first appeared, written by Saint John the Baptist in a Roman prison shortly before his execution, controversy has ensued about the meaning of the number. It is said to be the number of both Man and the Antichrist--which brings up a philosophical point (the relationship between man and the Devil et al.) not discussed here.
One theory has it that Tiberius (Nero), the cruelest persecutor of the Christians, is actually who John was talking about in Revelation. Under the Hebrew alphabet, words and letters can be placed with a corresponding number to form a string of code. Then, a mathematical operation is gone through, and the resulting number is a numerical name. When this process is done with Nero, his name turns out to be 666.
For Satanism, 666 represents the derision Satanists feel towards Christianity, and may also be taken to represent Nietzsche's Overman, as he was also referred to as "the Antichrist" in the book of the same name.
The Cross of Saint Peter originated as a Catholic symbol, and is still used on those churches whose saint is Peter. According to legend, Peter was crucified upside-down, because he denied three times that he knew Jesus Christ on the night of his crucifixion. He chose to do this, because he believed that his Saviour died facing heaven, and that a blasphemy such as the denial of Jesus would damn him to hell.

Satan is the equivalent of the Pagan god Pan. Pan is the symbol of fertility, virility, and power. Satan is often called the "Preferred Archetype", meaning that he is an unconscious symbol representing what Pan does as well. You can read more about archetypes in a later essay.