The number 666 is based on a Hebrew system of numerology called "Gematria" and refers to the sinfulness of man, as well as the rise of the "Beast," or Satan, as Jesus Christ prepares to return to Earth. It is mentioned in the last book of the New Testament, "Revelation."
Gematria is a system of numerology in which every letter of the Hebrew alphabet is assigned a numerical value and special meaning. For example, the number one refers to God who is complete in and of Himself. Seven is the number of completion because the Bible states that God created the world in seven days. Six is one less than seven and is therefore incomplete. Human beings were also made on the sixth day of creation. Because Adam and Eve disobeyed God, choosing to sin by doing what God forbade them to do, the number six is also associated with sin, particularly the sinful nature of human beings.
It was Satan, or the devil (in the form of a snake), who enticed Eve into sinning and she enticed Adam, so sin has long been associated with Satan. The Book of Revelation describes the last gasps of Satan, who has, since the beginning of time, sought to take over the world. Revelation 13:18 states: "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 is the King James Version and "threescore" is an archaic English version of 60. So, 666 is the sign of the devil because the number six represents sin and man's incompleteness.