In 1948, Jews and Arabs started shooting and bombing each other in Palestine/Israel. The UN, motivated by the nearly successful German attempt to kill all the Jews in Europe, had granted the Jews small bits of territory in British-administered Palestine and called the new country Israel. Although the British had controlled Palestine since 1919 and the Turks controlled it for a few centuries before that, the mostly Muslim Arabs that lived there quite reasonably considered it their land. They saw no reason that the sins of the mostly Christian Germans should be paid for with their land. The Jews, having lived for thousands of years in territory controlled by others, being severely repressed and eventually nearly wiped out, were determined to control their own country. The differences were irreconcilable so there was nothing to do but fight it out.
At the time there were about 50 million Arabs and only 100,000 Jews in Palestine, the Arabs had professional armies, the Jews had a few thousand veterans of World War II. Everyone thought the Arabs would finish the job the Nazi's started, but they were wrong. With help from Czech weapons, the Jews won the 1948 war and even captured significantly more territory than the UN granted them. Since then fighting between Israel and the Arab world has erupted periodically, with big wars in 1956, 1967, and 1973 and countless smaller conflicts.
The basic Arab strategy is to keep the conflict going (1). Israel is 300 miles long and 70 miles wide with a population of a few million. Arabs control all of North Africa and the vast majority of the Middle East with a population measured in hundreds of millions. Arab armies only have to win once and Israel will be destroyed, Israel has won again and again but cannot possibly develop the strength to occupy and control the vast Arab lands. Thus, even though Israel would be very difficult to conquer today, if the Arabs just keep the conflict going, eventually the military balance will change and Arabs will again control Palestine from the river to the sea.
Israel's strategy has been to build a crackerjack military to avoid a defeat leading to extermination and using this army to take territory they don't really need then trade it for peace. They traded the Sinai for peace with Egypt, and there's been no significant fighting for 40 years. They traded parts of the West Bank and Gaza for peace with Jordan and the PLO (2). There has been no fighting with Jordan, but peace with the PLO has not been complete. Israel even tried withdrawing from Lebanon and Gaza without a peace deal, but there is still fighting on both fronts. Nonetheless, the basic strategy is working fairly well. Although the vast majority of the Arab world, plus Iran, is still officially committed to the destruction of Israel and reclaiming the land they feel is rightfully theirs, the only immediate neighbors in that group are Lebanon (including Hezbollah), Syria, and Hamas-controlled Gaza. These have very short, easily defended borders with Israel. Furthermore, many Arab states have indicated they might agree to recognize Israel under various conditions.
There are only two ways for the Arab-Israeli conflict to end: the destruction of Israel, probably including killing or driving most of the Jews out of Palestine, or the Arab world accepting the loss of much of Palestine to Jewish control. Some advocate a democratic secular Palestine neither Jewish nor Muslim, where the rights of all citizens would be respected. One might remember, however, the Weimar Republic in Germany after World War I was a democratic country where the rights of all, including Jews, were respected and Germany had a long history of policy friendly to Jews. Nonetheless, within a couple of decades, the Jews of Europe were nearly wiped out by these same Germans. Jews would be fools indeed to willingly put their survival in the hands of others. If the Arabs want all of Palestine, they will have to fight for it.
There is a story that gets to the core of the Palestine/Israel situation. I don't know if it's true, but it's a good story nonetheless. One night shortly after the 1948 war a pregnant Jew in a kibbutz near the Egyptian border was killed. The tracks of the killers lead directly to an Arab village on the Egyptian side. A young Israeli officer was told to take his men to the village and a lot of Arabs were killed. A few days later there were outraged articles in newspapers around the world condemning Israeli atrocities in the village. The officer, distraught, went to David Ben-Gurion, the first Israeli prime minister. To the officer's surprise, Ben-Gurion was happy with the newspaper coverage. The officer asked why. Ben-Gurion said that for thousands of years killing Jews had been easy, safe, and painless; and the primary purpose of Israel was to make Jew-killing difficult, dangerous, and painful. The newspapers were helping spread the word.
That's what's going on in Gaza today. Hamas considers itself a religious organization (3) with a duty to destroy Israel, which they are too weak to do at present. To keep the fight going, Hamas launches rockets into Israel, occasionally killing a Jew or two. Israel is making that activity difficult, dangerous, and painful in hopes that, like Egypt, Jordan, and the PLO before it, Hamas and the rest of the Arab world will eventually give up trying to destroy Israel. That will end the Arab-Israeli conflict.
(1) This is why the 750,000 Palestinian refugees created in the 1948 war were never resettled anywhere in the vast Arab lands and millions of their descendants now live in crowded refugee camps. A few years earlier, in 1945 at the end of World War II, there were millions of refugees in Europe, all of whom have long since been resettled. Indeed, about 600,000 Jews were expelled from Arab lands in 1948 and fled to Israel, all of which have also long since been resettled even in tiny Israel. By refusing to resettle the Palestinian refugees, the Arab elite have cultivated a large population who, quite understandably, hate Israel. This helps immensely to keep the fight going.
(2) It should be said that all of these governments, Egypt, Jordan, and the Palestinian Authority, are fragile. They are all dictatorial, corrupt, or both and could be replaced by governments actively hostile to Israel. For example, Hamas won the last Palestinian Authority legislative election.
(3) This is important to understanding Hamas. For example, the ideal Muslim is the prophet Muhammad, and good Muslims often emulate his life. Muhammad was, among other things, a very successful warrior. At one point Muhammad made a ten year truce with his enemies. The people asked him why. He said that at the moment the enemy was too strong to defeat, but he could use the truce to build up his strength and defeat them, which is exactly what happened a few years later. This is why Israel is reluctant to negotiate a truce with Hamas.