The Christian faith believes in a Holy Trinity -- Father, Son and Holy Spirit. In Chapter 13 of Revelation John introduces us to the Unholy trinity -- the Dragon, the Beast out of the sea and the beast out of the earth. The Dragon is Satan, the beast out of the sea represents political power and the beast out of the earth has the power to perform signs and wonders (aka miracles). This unholy trinity is unleashed to overthrow the reign of God. The beast out of the Sea clearly meant Rome (seven hills of Rome = 7 heads/10 horns =10 Caesars) but would easily represent any and all coercive political regimes (Babylon, Alexander, Rome, The Ottomans, the Nazis. . . etc).
Emperor worship was required by the end of the first century as a symbol of loyalty to Rome. Politicians have used the uniting influence of religion to control and manipulate nations from the beginning of time. Worshiping the cult of the Emperor was considered an act of loyalty by citizens of the Empire. In the later century or so after Revelation was written, people were given a "proof of loyalty" document after performing the ritual and required act of emperor worship. One could not engage in trade or be employed without it. This economic persecution of the church was harsh. The ritual was simple, one went to the temple of the Emperor, burned a pinch of incense and declared "Caesar is Lord". Many Christians refused to do this because "Jesus is Lord" and believed this loyalty to be an act of idolatry. Notice the end of (10) "here is a call for the endurance and faith of the saints." Notice that in the verses preceding the saints are being conquered, having war made against them and generally being persecuted by the inhabitants of the earth for failing to prove their loyalty. Sometimes, on the Christian journey, God delivers us from the mouths of lions and frees us from oppression. Sometimes, on the Christian journey, we are called to be Purina Lion chow and have to endure, and even suffer, under oppression. As a resident of the United States, I do not know what that looks like. I have lived in easy religion my entire life and, frankly, what little push back we experience against the Christian faith in the U.S. is pathetically insignificant when compared to what others must endure. In nations and places around the world, Christians are imprisoned, beaten and killed because of their faith and trust in Jesus. We have it easy -- and the easy is one of the reasons our faith is weak.
In the ancient world slaves were branded with a mark that indicated that the person was owned by another. The book of Revelation plays with the image of "whose mark do you wear" in several places. The Christ followers are marked with a mark and their names are written in the "Lamb's book of life." Now, in 13 we encounter the "mark of the Beast" and the number 666 (in some Greek editions the number is 616). The critical thing is not the number but the purpose the of the mark. The mark identifies one as belonging to the Beast (slave or servant of the beast). The Christian will recognize that we want to bear in ourselves the ensign and mark that identifies us as belonging to Christ -- that mark is the water of baptism. Speculation on who the 666 (616) identifies is a matter of significant conjecture. Part of the problem is that the numerical identification does not work in English. In Hebrew and Greek there are no numerals -- each letter has a corresponding numerical value. Under that system each name has a corresponding number. It is widely believed that the 666 is a reference to Caesar Nero (whose name comes to that number when transliterated into Hebrew). Another way to look at is to note that the number 7 represents perfect completion (777 would be perfect perfection). The number 6 falls short of perfection and three sixes would be perfect imperfection . . . a way of saying that the beast is a caricature of the Lamb and requires wisdom to understand.