The Zionist movement was popularized by Theodor Herzl -- though he was not the first to put forward the ideas. But through Herzl's influence with his 1896 book, "Der Judenstaat" ("The Jews' State"), the Zionist cause focused on establishing a nation specifically for the Jewish people. The 19th century was a time of much nationalist fervor within European nations, and Herzl argued that the Jews of Europe would never be fully accepted or assimilated within Europe due to the anti-Semitism present in the European nations. So the Jews needed a nation of their own. From Herzl's point of view, that could have been accomplished by granting land for a state anywhere in the world. But the Zionist movement began to focus more and more on establishment of a Jewish state in the ancestral homeland of the Jewish people, which had come to be known as Palestine.
And that's chapter one of a whole course of study we could pursue on how the Arab-Israeli conflict began.