Region of Palestine (Palestine is a roman term for Judea, not a people) in 1919.
Zionism is the belief that the Jews have the right to re-establish (in modern times keep) their old Jewish homeland in Israel, corresponding to Canaan, Palestine, or Holy Land. Modern Zionism has had Theodor Herzl as one of its most-famous leaders, the movement emerged in the late 19th century and the early 20th century as anti-Semitism was at its strongest in the Russian Empire (which carried out pogroms against Jews and forced them into the "Pale of Settlement") and other European nations, with France accusing the Jewish man Alfred Dreyfus of passing military secrets to Prussia in the "Dreyfus Affair" and crowds yelling out "Death to the Jews!" in motions of racism. The Idea of Jews regaining independence in their homeland, however, has existed since the state of Judea lost its independence. In 1948. Israel became an independent country, immediately proving it by fighting a war of survival against its Arab Nationalist neighbors.
Zionist groups are many and have different ideologies beyond the fundamental belief in a Jewish homeland. Two of the most successful are Labor Zionists, which want the nation of Israel run under a left-wing bent, and the centrist or right wing Revisionist Zionists, which want Israel run in a right-wing fashion (the movement has become more centrist over time, however).