Someone correct me if I’m wrong but I believe the Church teaches that that was simply a number given to some Roman emperors of the time when Revelation was written. To be exact, I think it is the number of Nero’s name.
The Seer has marked the beast with the number 666. His purpose was that by this number people may know it. “He that has understanding, let him count the number of the beast. For it is the number of a man: and his number is six hundred and sixty-six”. A human number, i.e. intelligible by the common rules of investigation. We have here an instance of Jewish gematria. Its object is to conceal a name by substituting for it a cipher of equal numerical value to the letters composing it. For a long time interpreters tried to decipher the number 666 by means of the Greek alphabet, e.g. Iren., “Adv. Haer.”, V, 33. Their efforts have yielded no satisfactory result. Better success has been obtained by using the Hebrew alphabet. Many scholars have come to the conclusion that Nero is meant. For when the name “Nero Caesar” is spelled with Hebrew letters (NRVN QSR), it yields the cipher 666. N=50, R=200, V=6, N=50, Q=100, S=60, R=200; total, 666.
Here is a link to the Catholic Encyclopedia that has the entire article.