'This calls for a mind that has wisdom: the seven heads are seven mountains on which the woman is seated […] The woman you saw is the great city that rules over the kings of the earth.'
A point of contention in Christian circles is who 'Babylon' is meant to signify in the Book of the Revelation. Guesses range from a Revived Roman Empire, to the literal city Babylon, to the Vatican, to false religion in a general sense, and on and on. The guesses are probably in the hundreds.
John, the author of the Revelation, isn't vague, though. His symbolism doesn't try to hide the identity of what 'Babylon' is. He calls Babylon 'the great city' which 'has dominion over the kings of the earth'. Very specifically, he says in chapter 17 that Babylon 'sits' on 'seven hills'.
John wrote the Revelation in the late first century AD, in Asia, addressed to Asian churches, who were under the rule of the Roman Empire, and who were beginning to suffer persecution from Rome's emperor cult. Knowing that, read the following texts.
Cicero to Atticus, Letter 6
c 68-43 BC
6.5: You must certainly be at Rome by now. … When leaving the city of the seven hills [my wife's freedman] tendered an account of debts…
c 30 BC
2.535: So Rome became the loveliest of all things, and enclosed her seven hills with a single wall.
Virgil, The Aeneid
c 20 BC
6.781-783: Behold, my son, under his command glorious Rome will match earth’s power and heaven’s will, and encircle seven hills with a single wall, happy in her race of men.
Sextus Propertius, Elegies
c 20 BC
3.11-55-57: The city, high on its seven hills, that directs the whole Earth, was terrified of a woman’s power and fearful of her threats. … Celebrate a triumph Rome, and saved by Augustus beg long life for him!
Horace, Secular Hymn
c 17 BC
7, 11: A lofty hymn sung to those high gods that love our seven-hilled city … May you behold nothing greater than Rome's proud name.
c 10 BC
5.69: Rome, which sees the world from her seven hills, Rome, the place of empire and the gods.
c AD 100
4.64: On this side may you see the seven sovereign hills and take the measure of all Rome.
c 150 BC - AD 500
2.19: The people of seven-hilled Rome, and riches great shall perish, burned by Vulcan's fiery flame.
11.145-154: But when Italian soil shall generate, great wonder unto mortals, there shall be moans of young children by a fountain pure, in shady cavern offspring of wild beast that feeds on sheep, who unto manhood grown shall upon seven strong hills with reckless soul hurl many headlong down, in numbers both having a hundred, and their names shall show a great sign to them that are yet to be; and they shall build upon the seven hills strong walls and wage around them grievous war.
13.61: Reposing by the sacred water's side sends forth the appointed lot to seven-hilled Rome.
14.138: And many shall he utterly destroy in defense of the seven-hill city Rome, And for the sake of powerful sovereignty.
The city of Rome was known throughout the Roman Empire as 'the city of the seven hills'. The identity of Babylon in the Revelation is not up for debate. 'Babylon' was ancient Rome, the persecutor of John and his fellow Christians.