Babylon was an ancient city built on the Euphrates river in what is now southern Iraq. It once was the capital of a great empire which at one point conquered the land of Judah as mentioned in the second book of Kings and in Daniel. But the river changed its course and the city was abandoned long ago. Both the historic city in Mesopotamia and the parable city with its tower, mentioned in Genesis, represent the same thing, a worship that appears holy in externals, while the internals are profane. This representation expands to mean a church whose leaders use this kind of worship to gain dominion over others for their own gain and for the gain and power of the church. The city itself is the doctrinal structure that supports this kind of worship and dominion.

(References: Apocalypse Explained 1029; Arcana Coelestia 1283, 1302, 1304, 1310, 1311)

The meaning of "believe" in the Bible is pretty straightforward, but runs deeper than what appears on the surface. When in the Old Testament people were called on to believe in Jehovah, it meant a belief that Jehovah would lead them in spiritual things, not just natural ones, that following Him would lead to spiritual life. When people believed in Jesus in the New Testament, it meant believing in Him fully, as God Himself, all-powerful. Implied in this level of belief also was belief in what He taught and the importance to follow His precepts. That's why Peter sank while walking on the water; he began to see the human element of Jesus rather than God himself. It's also why Jesus could not do miracles in his home area; people there had known Him as a boy and young man, and could not believe in Him as God.

(References: Arcana Coelestia 6956, 6969, 6970, 7065, 8240, 8783, 10392; The Apocalypse Explained 815 [2-15])