In the Bible, exile is the deportation of population groups of a defeated nation to a place designated by the conquering nation. Several deportations into exile are referred to in the Old Testament. People from the (northern) kingdom of Israel were exiled by the Assyrians to various places in Mesopotamia after the fall of the capital Samaria in 722 BCE (2 Kgs 17:6). People from Judah were exiled by the Babylonians to Babylonia after the surrender of King Jehoiachin of Judah in 598 BCE (2 Kgs 24:14-15), and again after the fall and destruction of Jerusalem in 587 BCE (2 Kgs 25:11), and a third group in 582 BCE (Jer 52:30).
The term ‘the Exile’ normally refers to this exile of Judaeans in Babylonia, and to the period between the fall of Jerusalem (587 BCE) and the conquest of Babylon by Cyrus of Persia in 539 BCE, when Jews began to be permitted to return home, according to Ezra 1.
The Israelites deported by the Assyrians are not heard of again (hence the legend of the ‘Ten Lost Tribes‘; in actuality most of the people continued to live in their homeland). Those deported by the Babylonians became a flourishing community, and remained so until 1948 CE. Many of them, however, returned to their homeland at various times: see the books of Ezra and Nehemiah. It is likely that these returned exiles were key players in the editing of most of the books of the Old Testament and the establishment of the Jewish religion.
By the process of restoration, post-exilic Jewry was given hope and directives to regain their relationship with God by righteous living via the various prophecies, often in the form of eschatology.