Zionism is the belief that Jews as other nations have the right for self-determination. It is the political idea and movement to (re)create homeland for the Jews in their ancestral homeland in "Eretz Yisrael", that is in the Land of Israel.
The word Zion is one of the many names of Jerusalem.
The idea of returning to the Jewish homeland has been part of the Jewish identity for more than 2000 years since the Jews were expelled in various ways from that area. Jews throughout the history always maintained some presence in the area and there were always individuals and small groups of Jews who moved to the are called Eretz Israel. The especially lived in Jerusalem, Tzfat, and Hebron.
In second part of the 19th century along with the European national movements Herzl started the Zionist political movement to recreate the Jewish homeland.