The main issue is land and who is in control of it. The conflict between Israel and Palestine began in regard to the creation of the State of Israel. Palestinians and Arab nations in the region did not welcome the establishment of a Jewish state on what had for centuries been Arab territory.
Details/context:
There had been Jewish immigration into the Palestine region since the end of the 19th century. The movement of Jews back to what they saw as their ancestral territory escalated with the Zionist movement in the early 20th century. Persecution against Jews in Europe (notably, pogroms in Russia in the 19th century and the Holocaust perpetrated by Nazi Germany in the 20th century) increased pressure for Jews to leave European countries.
The Palestine region had been part of the Ottoman Empire up until the end of World War I. A mandate system authorized a member nation of the League of Nations to govern a former German or Ottoman colonial area after the conclusion of World War I. The former Ottoman provinces of Syria, Iraq and Palestine in the Middle East were divided into a French mandate territory and British mandate territory. The British exercised mandate rule over Palestine.
After the Second World War II ended in 1945, the United Nations (UN) adopted a plan for the partition of Palestine that would create a portion of that territory as the state of Israel, with the other part as an independent state for Palestinian Arabs. The Arabs in the region and surrounding Arab nations were not in favor of this, because they opposed the creation of a Jewish state in their region.
As the British were ending their mandate governance of the region in May, 1948, the Jewish leaders in the land proclaimed their independence as a nation. A war with Arab peoples and nations in the region followed. Israel won that war and established itself as a nation. Over 700,000 Palestinians fled their homes and land and have not been able to regain independent rights to their territory.
The new state of Israel was granted membership in the UN in 1949. Israel won a series of wars (in 1967, 1973 and beyond) over against Arab states in the region. Palestinians have made efforts against Israeli control, notably with movements called "Intifadas," in 1987 and 2000. They have not been able to achieve nationhood status, however.
