Historic Palestine or the Land of Israel. (Both are regional names for the same piece of land, roughly.)
It depends on the particular conflict, but the two territories most in contention between the Israelis and Palestinians are the Gaza Strip and the West Bank (including East Jerusalem). There is much contention between Israelis and Syrians over the Golan Heights and between Israelis and Lebanese there is some contention over the Shebaa Farms and the area south of the Litani River. It is important to note that while Israel is the Jewish State, its soldiers and citizens are Israelis and have important non-Jewish components. (This is why the word Jew has not been used above in favor of Israeli.)
Palestinians are those Arabs who trace their origins to the former British Mandate of Palestine, so that area could be considered their homeland. However, it is worth noting that prior to 1993, there was no Palestinian self-rule at any time in history when the identity (or its Levantine Arab predecessor) existed.
It is important to note that the military/paramilitary conflict is between Israelis and Palestinians, not Jews and Palestinians since the Israeli Army contains more than just Jews. Israelis and Palestinians are still fighting because neither group has achieved their objective. The Israeli objective is to have a dominant state in the region, living in peace with its neighbors, and with borders that are secure. The Palestinian objective is to have an independent government, international relations, and freedom of movement for its inhabitants. Unfortunately, both of these objectives are greatly expanded by fanatics on both sides who see the only possible implementation of these ideals being one in which the other party cannot exist or exists in such a weakened and defeated state that there can be no real peace. This is why the conflict continues. To see the causes and desires fueling the Israeli-Palestinian Conflict in more detail, see the related question.
Not every Israeli thinks the same way and you can find a wide variety of opinions across the Israeli political and social spectrum. Some Israelis think that the Palestinians are to blame and that the Palestinians as a group and Arabs as a whole cannot imagine the possibility that someone other than them has a right to govern any area in the Southern Levant. There are other Israelis who think that the entire conflict would end if Israel would only retreat from the Occupied Territories in the West Bank and withdraw all of the settlements. Most Israeli opinion, though, is somewhere in the middle, faulting both Palestinian Militants and Israeli Government Intransigence.
There are isolated skirmishes between Religious Zionists and the Israeli Army. These come as a result of the Religious Zionists belief that Jews are promised all of the territory of the Land of Israel by God and therefore Palestinians are not entitled to any of it whereas the Israeli government has made concessions to the Palestinian Authority for peace. However, most of the confrontations are not between Israelis and Jews, but between Israelis (who are themselves mostly Jewish) and Palestinians. This conflict is described in more detail in the Related Question.
The Old City of Jerusalem is known for its sacred sites in the Jewish, Muslim, and Christian faith, solidifying each group's historical claim to the land. Both the Palestinians and Israelis want Jerusalem as their capital.
It depends on the particular conflict, but the two territories most in contention between the Israelis and Palestinians are the Gaza Strip and the West Bank (including East Jerusalem). There is much contention between Israelis and Syrians over the Golan Heights and between Israelis and Lebanese there is some contention over the Shebaa Farms and the area south of the Litani River.
It depends entirely on who is doing the supposing. Palestinians argue that they are supposed to live in the places that their families used to live in 1946. Israelis argue that they are supposed to live in Jordan or in the Palestinian Territories.
It depends on the particular conflict, but the two territories most in contention between the Israelis and Palestinians are the Gaza Strip and the West Bank (including East Jerusalem). There is much contention between Israelis and Syrians over the Golan Heights and between Israelis and Lebanese there is some contention over the Shebaa Farms and the area south of the Litani River. It is important to note that while Israel is the Jewish State, its soldiers and citizens are Israelis and have important non-Jewish components. (This is why the word Jew has not been used above in favor of Israeli.)
Palestinians are those Arabs who trace their origins to the former British Mandate of Palestine, so that area could be considered their homeland. However, it is worth noting that prior to 1993, there was no Palestinian self-rule at any time in history when the identity (or its Levantine Arab predecessor) existed.
There are quite a number of such sites, but the most famous is the Temple-Mount/Noble-Sanctuary area in the Old City of Jerusalem. It is the holiest site in the world to Jews and the third holiest site in the world to Muslims.
It is important to note that the military/paramilitary conflict is between Israelis and Palestinians, not Jews and Palestinians since the Israeli Army contains more than just Jews. Israelis and Palestinians are still fighting because neither group has achieved their objective. The Israeli objective is to have a dominant state in the region, living in peace with its neighbors, and with borders that are secure. The Palestinian objective is to have an independent government, international relations, and freedom of movement for its inhabitants. Unfortunately, both of these objectives are greatly expanded by fanatics on both sides who see the only possible implementation of these ideals being one in which the other party cannot exist or exists in such a weakened and defeated state that there can be no real peace. This is why the conflict continues. To see the causes and desires fueling the Israeli-Palestinian Conflict in more detail, see the related question.
At various times the Palestinian people are referred to as refugees. In some cases it's a clear and correct choice. Many Palestinians live as refugees in Jordan or in Gaza. Also, the Palestinians are living in land they claim as their own, that would be Israel. Although they live in a territory they believe is their homeland, the area is now technically speaking, and that's also a reality, living in a nation that is controlled by the Israeli government. In that sense, they could be called refugees. With all that said, the Palestinians living outside of Israel are refugees. As an aside, the term Palestine, is a name given to that territory by the Romans, when they controlled the eastern Mediterranean Sea. They had dispersed the Jews living there as a punishment for the "problems" they caused to the Roman empire under Hadrian.
Not every Israeli thinks the same way and you can find a wide variety of opinions across the Israeli political and social spectrum. Some Israelis think that the Palestinians are to blame and that the Palestinians as a group and Arabs as a whole cannot imagine the possibility that someone other than them has a right to govern any area in the Southern Levant. There are other Israelis who think that the entire conflict would end if Israel would only retreat from the Occupied Territories in the West Bank and withdraw all of the settlements. Most Israeli opinion, though, is somewhere in the middle, faulting both Palestinian Militants and Israeli Government Intransigence.
They are two different cultures. Palestinians are generally Arab Muslims, with roots in the area going back to at least the Byzantine era, if not longer. Israelis are generally Jews of all ethnicities, traditionally believed to be the descendants of the diaspora come back to the "Promised Land" of Moses. Each has a strong argument as to why they should be there, but only the Israelis have had recognized legitimacy from the Western World, especially the US.
Palestinian AnswerAll of the nation that was once Palestine, a land holy to all 3 major monotheistic religions. They want to control it as if it was theirs, given the land was originally the Palestinian Arab's land. The Israeli Jews claim that the land was theirs a long time ago, however, they are kicking the rightful Palestinian civilians that live their innocently to claim a land that's not theirs.Israeli AnswerIsrael is a diverse country and home to a vast number of opinions. There are certainly those who wish to control all of the land of the British Mandate of Palestine, but that is not the majority. The majority of Israelis wish to control the area inside the 1949 borders with a few land-swaps with the Palestinians to provide for more defensible and realistic borders. For most Israelis, the question is not about land-control, it is for peaceful borders and peaceful neighbors.
The Israelis have more powerful weaponry than the Palestinians. -- Israel is a nation, with a parliamentary government comprised of democratically elected representatives, a highly respected judicial system, a first-world economy, and a strong military comprised of army, navy, and air force elements. -- "The Palestinians" are just that ... a group of people, living on lands that are parts of Lebanon, Jordan, Egypt, and Syria, none of which countries grant them citizenship, under one government elected 10 years ago, and another one that conquered part of their area by violent force, with a marginal economy propped up by support from the Arab countries, the USA, Israel, and others, and certainly without any organized military establishment.