The Babylonian Exile was the exile of the Jewish people to Babylon by Nebuchadnezzar II. By this time the Kingdom of Israel had already fallen over 100 years earlier to the Assyrians, leaving only the Kingdom of Judah as an independent Jewish entity. Under Nebuchadnezzar, the first deportation took place in 597 B.C. followed by another when Judah was overrun by the Babylonians and ceased being a nation in 586 B.C. The Book of Jeremiah in the Bible records a third exile 5 years later as well.
When Babylon was conquered by the Persians, the Jews were later allowed to return to the land of Israel starting in 536 B.C., but were still under foreign occupation.