Fighting in the region of Israel, Palestine, and the Gaza strip comes down largely to land disputes and the concept of nationhood. After the events of World War II the United Nations established the country of Israel (May 14th 1948) to serve as a safe haven for Jewish communities facing frequent persecution in Europe. The problem was that in order to create the state of Israel land that had already been claimed by the Palestinians and other Middle Eastern groups had to be taken. Both sides claim ancestral lineage to the region particularly with regard to the holy city of Jerusalem.
The Palestinians claim the land is theirs as prior to the creation of Israel they had occupied the region for hundreds of years yet they are not a recognized state by nearly every western nation of the United Nations. The Jewish claim dates back to the roman era when they were displaced from the land by the expanding empire but had not occupied the land in force for over a millennia after. The Gaza strip, together with the West bank constitute the territories claimed by Palestine and the defacto Palestinian state now recognized by 135 members of the United Nations (largely Africa, Asia, and South America). First captured by Israel in the Six Days War in 1967, the Gaza strip has been the scene of frequent conflicts between Israeli and Arab forces.
The overall conflict comes down to Israel's refusal to recognize Palestine as an independent state and the Palestinian's demands for land claims in regions currently occupied by Israelis. The religious differences between the two states are a significant factor in why relations and agreements between them tend to break down.