An exile is someone who was forced out of their home country and is now living somewhere else. Adam and Eve were exiled from the Garden of Eden because of sin (Gen 3:23,24).
The Jews were forcibly taken captive by King Nebuchadnezzar of Babylon. They experienced several progressive deportations between 607-586 BC as recorded in 2 Kings and 2 Chronicles. God used Babylon as His agent of judgement against Israel for their sins of rebellion and idolatry. Jerusalem was attacked and left in ruins with many killed and thousands taken captive, including Daniel and the other young men who were later thrown into the furnace (Dan 1:1-8). After 70 years of exile, the Jews were permitted to return and rebuild the city and temple under the direction of Ezra and Nehemiah. In 70 AD the Romans again exiled the Jews.
These accounts show Biblical exile is because of sin, and results in a separation from God because sinners must be separated from God (Isa 53:6, 59:2). Yet He doesn't want separation from mankind who because of our waywardness are in this self-imposed isolation. God imposes exile to spur repentance in the hearts of those who having known the closeness of relationship with Him. His aim is the banishment will stir the desire and motive to return to the position they have forfeited because of sin.
Jesus dying in our place for our sin which had caused a separation with God, was crucial as this made it possible for our being restored back into fellowship with God. However, salvation is not forced on anyone; we must choose to come back into relationship through repentance, the turning away from sin (Jn 1:12; 1 Pet 2:25).
Have I returned to relationship with God?
ultimate long-term answer to this the most crucial and eternal dilemma facing mankind (Jn 3:16; Rom 3:23, 5:8, 6:23).
The apostle John was exiled on the island of Patmos, not because of his sin but as a means of persecution by the Roman authorities (Rev 1:9). It was here, being banished from society he was given various visions which are recorded in the Bible as the book of Revelation (Rev 1:1,4).