The history of the Jewish people begins with Abraham, and the story of Abraham begins when G-d tells him to leave his homeland, promising Abraham and his descendants a new home in the land of Canaan. (Gen. 12). This is the land now known as Israel, named after Abraham's grandson, whose descendants are the Jewish people. The land is often referred to as the Promised Land because of G-d's repeated promise (Gen. 12:7, 13:15, 15:18, 17:8) to give the land to the descendants of Abraham.
The land is described repeatedly in the Torah as a good land and "a land flowing with milk and honey" (e.g., Ex. 3:8). This description may not seem to fit well with the desert images we see on the nightly news, but let's keep in mind that the land was repeatedly abused by conquerors who were determined to make the land uninhabitable for the Jews. In the few decades since the Jewish people regained control of the land, we have seen a tremendous improvement in its agriculture. Israeli agriculture today has a very high yield.
Jews have lived in this land continuously from the time of its original conquest by Joshua more than 3200 years ago until the present day, though Jews were not always in political control of the land, and Jews were not always the majority of the land's population.
The land of Israel is central to Judaism. A substantial portion of Jewish law is tied to the land of Israel, and can only be performed there. Some rabbis have declared that it is a mitzvah (commandment) to take possession of Israel and to live in it (relying on Num. 33:53). The Talmud indicates that the land itself is so holy that merely walking in it can gain you a place in the World to Come. Prayers for a return to Israel and Jerusalem are included in daily prayers as well as many holiday observances and special events.
Living outside of Israel is viewed as an unnatural state for a Jew. The world outside of Israel is often referred to as "galut," which is usually translated as "diaspora" (dispersion), but a more literal translation would be "exile" or "captivity." When we live outside of Israel, we are living in exile from our land.
Jews were exiled from the land of Israel by the Romans in 135 C.E., after they defeated the Jews in a three-year war, and Jews did not have any control over the land again until 1948 C.E.