If you want a simple answer it's a number from the Christian Bible which is the Beast's number. Who is the Beast, most Christian's would say it's the symbol for the anti-Christ, who comes in Armageddon, even though the actual title of anti-Christ is only mentioned maybe twice in the Bible itself. Other researchers suggest it was for the Roman Empire because of all the oppression the Jewish people were put under for their faith, and later the Christians. It's also seen as a number to identify who can buy and sell under the anti-Christ regime.
It can also be seen as a magickal number:
(Wikipedia)
"666 is the magic sum, or sum of the magic constants of a six by six magic square, any row or column of which adds up to 111."
and
It is the sum of the first 36 natural numbers (i.e. 1 + 2 + 3 + ... + 34 + 35 + 36 = 666) for you nerds :)
For the same reason people avoid 13s or cross their fingers for a 7? It's just media hype. If someone famous in the church were to do something good and say the number 666 gave him the knowledge to do his deed, there would be a big shift in number superstition. It's just a number. No power (unless it's on a check with my name on it in the pay to the order of line)
This should go in the "song lyrics" disscussion, but I find it strangely fitting, so I'll just leave this here...
Slow Numbers
by Morphine
Lazy boys and shy Dianes. One at a time, single file.
They counted the low numbers as they walked by.
I count a high number. Of low numbers. Among the slow numbers.
The number four means nothing to me but the number four means death to Chinese.
Number seven is lucky in Japan. Here we don't give a damn.
But on the elevator, no thirteenth floor.
On the elevator, no thirteenth floor.
Thirteenth going up. Going up... Going up...
As ShadowMoon says, it's from the Bible. To be precise, it's in the Revelation of St. John the Divine (commonly called "Revelations"). It is full of mystical prophecy and is excellent crazy-fuel. The Hebrew alphabet and the Greek alphabet are both very useful for numerology, and the general view is that St. John wished to communicate something that would be understood by his contemporaries, but occult to the princes and powers. Both alphabets use letters to signify numbers, so it's easy to convert names and words into numbers, and vice versa. In my view you can "prove" anything by numerology. It's about as demanding as making a pun.
When I was brainwashed into christianity by my family, I was told it was the number of the anti-christ and that we would all have to get it tattoed on our foreheads in order to be able to buy food, receive medical care, etc. And if we didn't, we would be "slain in the name of Jesus." It's just a bunch of christian propaganda, to scare people into being christian. One would have to believe in the bible for it to carry any weight.
The "tattoed on your foreheads" people have a wonderful source of ammunition. Bar-codes all include a check-setting, to make sure the thing is working properly. This is the number "666". So all bar-codes have it. Spooky, eh? Cue X-files music, bible-thumpers, etc.
It's a serious OOPS by the Christians, it's a numerogical mishap.
On the Dead sea scrolls it says something like 616; many Churches played out the Hellfire and Brimstone act because too much truth in information out there.