This conflict, in theory, is actually a centuries old fight for a small patch of land, The Gaza Strip and Jerusalem. The modern version of this all started at about 1947, right after World War II ended. The United Nations decided to give the Jewish people this land after their persecution by Hitler during the War. Jews began moving into Palestinian land, starting two year war. At the end of the war, the newly founded nation of Israel had taken over huge portions of once Palestinian land, creating hundreds of thousands of refugees and a huge amount of tension between the Arabs/Palestinians and Israel. The conflict between the Arabs and the Jews has been an on and off fight for decades, waging fierce battles and wars. Neither nation wants to quit, and neither appears to be willing to back down.
The Six-Day War
After Israel had been founded there was a twenty year period where no wars where fought between the Israelis and the Palestinians. Then finally in 1967, the Six-Day War broke out, and Israel finally invaded and took over the West Bank and Gaza Strip, eliminating the remaining evidence of Palestine. This further escalated conflict between them, and was controversial too since Israeli forces accidentally attacked and American war ship, the USS Liberty. New waves of Palestinian refugees were creating during this time, further increasing world problems.
A map of land holdings around Gaza Strip.
Today, there are still millions of refugees held in camps around West Bank, Gaza Strip, Jordan, Syria, and Lebanon. In 2005, Israel left Gaza and a group widely regarded as terrorists called Hamas took over. They violently fight to take back Palestine's old holdings from Israel and refuse to recognize Israel as a sovereign nation. Israel has blockaded Gaza off, and life for the 4.6 million residents within it is rough and harsh, as Israeli people treat Palestinians within Gaza poorly.
Progression towards peace
Today, there have been a few breakthroughs in creating peace in this troubled area. The United States has worked very hard with it's ally, Israel, to try and create a lasting peace between Hamas, the Palestinians, and Israel. Palestinians want Gaza and West Bank to become a new country, Palestine, Hamas wants to obliterate Jewish views and Israel, and Israel wants it's people to feel safe and for Hamas to acknowledge Israel as a nation and stop aggression. Above all, they want their religious holy land and most of all the city of Jerusalem. As of today, there is no visible peace to this conflict as all their needs conflict with each other but one day, peace will hopefully come.