Although they did not have their own country, the Palestinians who inhabited the area we now call Israel were their own ethnic group.
During the 1940's there was a mass migration of Jewish people going to a British mandate previously owned by the ottoman empire before its collapse, they went there because of a landmark holy to the Jewish people, the west wall, was there.
When the Jewish people moved to the British mandate the Palestinians saw this as an attempt from Europeans to take their land and fought against the Jewish settlements, because of the excessive fighting Britain gave the Jewish people their own country,Israel, they then gave the mostly Palestinian areas, the west bank and Gaza strip, to Egypt and Jordan, the surrounding Arab nations.
the surrounding Arab states were not happy with Israel becoming a country and waged war on Israel, during this war Israel gained more land including the aforementioned West Bank and Gaza strip, but these areas were not completely under Israeli control as the Palestinian rebels lived there
the most popular solution to the issue is a two state solution where both Palestine and Israel get a country, but the main issue is that there Palestinians feel that since it was their land first they should have possession of it Hamas the terrorist group in control of the strip is the main group promoting this idea.