The quick answer to this question is that the tension between the Palestinians and the Israelis was caused by the creation of the State of Israel in land that had belonged to the Palestinians. Let us look at this process in more detail.
Before WWI, the area that is now Israel was part of the Ottoman Empire. When the Ottomans were on the losing side in the war, their empire was divided up by the League of Nations. Britain was given the mandate to administer Palestine for the League. Before this, one part of the British government had promised support for an independent Arab state in the area while another had promised to support the creation of a Jewish homeland. Jewish Zionists believed that Palestine should rightfully be their homeland based on their occupation of that area in Biblical times.
The promise of a Jewish homeland brought Zionist settlers to Palestine, where they came into conflict with Palestinian Arabs. This influx of Jews increased as Hitler came to power in Germany. WWII then came about, bringing with it the Holocaust, which led to increased Western support for the idea of a Jewish homeland.
After WWII, the British government gave up the Palestinian Mandate to the United Nations, which proposed splitting it into a Jewish country and an Arab country. When the British pulled out, the Zionists proclaimed the State of Israel and surrounding Arab countries invaded in an attempt to get the land for themselves. The negotiations that ended this war set up the State of Israel, with control of everything that is now part of that country while other parts of the Mandate were controlled by Jordan (the West Bank) and Egypt (Gaza Strip). The Palestinians themselves were not given control of any territory. As Israel was being created, many Palestinians either fled the area that was to become Israel or were expelled by the Israelis.
The other major events that helped lead to the Munich Massacre were the creation of the Palestine Liberation Organization (PLO) in 1964 and the Six-Day War in 1967. The creation of the PLO gave the Palestinians and organized representative that was willing to engage in terror to try to oppose Israel. The Six-Day War heightened tensions between the Israelis and Palestinians because, in that war, Israel took control over the West Bank and Gaza. The Israelis now controlled all of the land that had been part of the Mandate and the Palestinians did not have real control over any of that land.
The terrorist attacks on Israeli athletes during the 1972 Summer Olympics were caused by tensions between Israelis and Palestinians that arose because of the creation of the State of Israel and because of Israeli control over all of the lands that the Palestinians considered to be their own.