From the Book of Revelations:
13:16 And he causeth all, both small and great, rich and poor, free and bond, to receive a mark in their right hand, or in their foreheads: 13:17 And that no man might buy or sell, save he that had the mark, or the name of the beast, or the number of his name.
13:18 Here is wisdom. Let him that hath understanding count the number of the beast: for it is the number of a man; and his number is Six hundred threescore and six.
This single mention has sparked endless speculation and interpretation in Christian as well as magical circles. We can make the following observations:
Six is repeated three times. Six is one less than seven and seven is traditionally the number of completeness or divinity. In this sense, we could see the number as a symbol of the not divine to claim the status of the divine trinity by repeating the number three times. In the text it is said that this is the number of a man, which would support this idea.
Numerologically, 666 resolves to 9. (6+6+6 = 18, 1+8=9) Nine often symbolizes repetition and cycling. Incidentally, any multiple of nine resolves numerologically to nine. In this sense nine could be seen to be a number of entrapment, referring to endless repetitions of the cycle of third density.
One of the more original interpretations of 666 is found in the Cassiopaea material, where 666 is said to refer to VISA. VI is six in roman numerals, S is six in ancient Egyptian numerals and A is six in Sanskrit. This refers both to a system of global credit and debit, as in the Visa card, well fitting with Rev. 13:17 above. The other apparent meaning is that a visa is required for prolonged stay in foreign countries. So the symbol refers to both control of exchange as well as control of travel.
Additionally, numerological correspondences of diverse names with 666 have been sought throughout history. Sometimes 666 has been claimed as a title or epithet by would-be magicians or Satanists.
See Cassiopaea transcripts.