There are many intertwined causes of the Israeli-Palestinian conflict. These causes tend to be religious/ethnic and historical in nature. Let's look briefly at each.
Most Israelis are Jewish. Most Palestinians are Muslim. Within the Israeli population, there exists a contingent of fundamentalist Zionists. They see themselves as the protectors of a biblical vision of Israel in which the entire region is divinely destined to be the Jewish nation. This includes the restoration of the Jewish Temple on the Temple Mount in Jerusalem. This holy site is also sacred to Muslims. It is believed to be the location from which Muhammad ascended to Paradise. Fundamentalist Muslims see the whole region as part of a holy territory that must be "liberated" from the control of non-believers. These antagonistic religious views of the same territory have naturally led to protracted conflict.
Although the current conflict originated in the twentieth century, both Jews and Palestinian Arabs have historic claims in the region dating back millennia. Palestine had been the Jewish nation until most were expelled by the Romans in the first century CE. After World War II and the Holocaust, Jewish refugees from Europe wanted to join their remaining brethren in Palestine and create a Jewish homeland in which they would be free from the persecution that they had experienced for countless generations during the Jewish diaspora. The Arab majority there resisted this idea. In an attempt to prevent conflict, the United Nations partitioned the territory between Palestinians and Jews in 1948. Palestinians and the neighboring Arab nations rejected this plan and invaded. They were pushed back by Israeli forces, which then seized additional territory. In 1967, Israel's Arab neighbors attempted to invade again. This backfired and Israel seized additional territory including the Gaza Strip and the West Bank. This has resulted in over four million Palestinians living as refugees within these occupied territories. Israeli have established numerous "settlements" in these areas, which further antagonizes Palestinians who see themselves as refugees in their own land.