What does it mean that Jews were exiled?

Answer 1

The Jews were in exile several times in their history, they were in exile in Egypt during Moses time, in the time of Daniel, and also under the Babylonians under Ezra.And they had to come back home each time.

Answer 2

"Exiled" means kicked out of their homeland. The prophets had constantly warned the Israelites that ignoring the Torah would result in exile.
1) Around 2600 years ago, the Assyrians forcibly exiled the Ten Israelite tribes to points unknown. A small percentage of each of these tribes is still among us, but most of them were exiled and didn't return.
2) Around 2500 years ago, the Babylonians destroyed the First Temple and forcibly exiled the remainder of Israel's population to Babylonia. (See: The Destruction)
While the Jews were permitted to return to Israel (Judea) seventy years later, and tens of thousands did so (and rebuilt the Temple), most of them remained in Babylonia, while others began to settle in North Africa, southern Europe, the Crimea, throughout the Near East and elsewhere.

3) In 68 CE, the Romans destroyed the Second Temple. The Romans did not force the Jews out of Judea in a single expulsion. Rather, the Romans expelled them from Jerusalem only; and the rest of Judea lost its Jews slowly, over a period of centuries, as living there became too harsh. Even then, we have records of Jewish communities who lived in Judea (Palestine) during the entire period of the last two millenia. (See:History of the Jews in Israel)

Those Jews who left Judea went to southern Europe, North Africa, Arabia, the Near East, and (slowly) further afield (especially throughout Europe).

See also:

Jewish history timeline

Where do Jews live today?