"Here is wisdom. Let him who has understanding calculate the number of the beast, for the number is that of a man; and his number is six hundred and sixty-six," (Rev. 13:18).
666 is the number of the antichrist, the end-times figure who will arise with the purpose of opposing God and God's people. 666 is the gamatria of the name of the antichrist.
In Greek and Hebrew there are no numeric characters. There are only alpha characters. For example, the letters a, b, c, d, e, f, etc. are alpha characters. The numbers 0, 1, 2, 3, etc., are numeric characters. They are different--except for the letter "o" and the number "0". When the Greeks wanted to write a number, they used letters for numbers. The Greek letter "alpha" had the numeric equivalent of 1. The next letter "beta" has the numeric equivalent of 2, and so on. (CARM has a chart of the Hebrew and Greek numeric equivalents if you are interested in more information.)
Therefore, whenever a word in Greek is written, because the letters are also numbers, every word has a numeric value. This numeric value is called a gematria. The Greek word for Jesus (iasous, Ἰησοῦς) has a mathematical equivalent of 888. Also, the Greek word for fish (ichthus, ἰχθύς) is 1224.
The Bible is saying that the future antichrist will have a name that, when written in Greek, will have a numeric equivalent of 666.