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.)
Israeli Arabs have the same rights as Israeli Jews and therefore can choose to live wherever they want within Israel or Area C in the West Bank. Unlike Jews however they can also settle in Areas B and A where Jews are prohibited to enter by law. However few Arabs choose to live in settlements, except for Ariel where many Arabs study in the Shomron Academic Center, and few Jews in Judea and Samaria would like to have Arabs for neighbors.
In the autumn of 1917 the British Army was advancing into Palestine, then in the Ottoman Empire. The Balfour Declaration (dated 2 November 1917) was a statement that the British government viewed 'with favour the establishment in Palestine of a national home for the Jewish people, ... it being clearly understood that nothing shall be done which may prejudice the civil and religious rights of existing non-Jewish communities in Palestine ...' (It should be noted that Palestinereferred to the area now covered by both Israel and Palestine). After World War I the area was placed under British rule. There were difficulties from an early stage (the 1920s) because the establishment of a 'national home for the Jewish people' was widely seen as in conflict with promises made to the Arabs in the area. Soon fighting started between Arabs and Jews.
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 State of Israel is not an illegal country. Nor was it established by force. The British took contol of the Region called Palestine (the name was given by the Romans) after the collapse of the Ottoman Empire. The British set aside the current state of Israel (including Judea and Samaria (known to some as the West Bank) in the Balfour Declaration in 1917. It took another 30 years before the United Nations declared two states for the region on November 29,1947. A state for Jews and and a State for the Arabs who lived in the Area.
After WWII, Jews were settled in a state controlled by Palestinian Arabs, a move supported by most of the European nations and the US. in the 1960's, the Jews took over the state militarily and turned it into the current Jewish state of Israel, driving many of the Palestinians out of the region and turning the rest into a largely disempowered minority. Most Arabs see the state of Israel as an illegitimate state imposed on the region by western powers in an effort destabilize the surrounding Arab/Muslim states and believe it should be removed (much the way the US saw the Iraqi take-over of Kuwait as illegitimate and took steps to remove it). add several centuries of conflict between Arabs and Europeans (the various European crusades and expansions of the Ottoman empire), where Jews are largely considered by Arabs to be European rather than semitic. =========================================== The following facts were apparently dropped from the above account because of some sort of computer error: 1). the continuous Jewish presence in the area since roughly 1200 BCE; 2). the stated policy of the British government 20 years before WWII that some part of the mandate administered by the British in Palestine ought by rights be re-designated a modern Jewish homeland; 3). the resolution by the majority of the UN General Assembly in 1947 to partition the western extremities of the British mandate into regions administered respectively by Arab and Jewish interests, in endorsement of the British policy; 4). the declaration of independent statehood by Israel in 1948 (not "the 1960s"), and its subsequent recognition by all but about 30 UN members; 5). the property, economic, voting, and legal rights of the "largely disempowered minority", including its several elected representatives in the national parliament.
Primarily the lower Levant, typically called Israel-Palestine.
Israeli Arabs have the same rights as Israeli Jews and therefore can choose to live wherever they want within Israel or Area C in the West Bank. Unlike Jews however they can also settle in Areas B and A where Jews are prohibited to enter by law. However few Arabs choose to live in settlements, except for Ariel where many Arabs study in the Shomron Academic Center, and few Jews in Judea and Samaria would like to have Arabs for neighbors.
Israel
The UN did, way back in 1948. It voted to split Palestine, which was then the name for the area overall, into two parts. One, which would include Jordan, would be the home for the Arabs in that area. The second would be the home for Jews, namely Israel. Israel immediately accepted that and declared itself a state (country). The US was the first country in the world to recognize Israel as a new country. But the Arabs, despite having many, many countries in the area, most very large, wouldn't tolerate Jews having even a tiny country within the Middle East, so Arab countries banded together and attacked the new Israel. There were huge numbers of refugees in both directions, with many hundreds of thousands of Jews being forced out of the Arab countries, and many hundreds of thousands of Arabs leaving the area that was now Israel. The Arabs say that the Israelis forced them out, and the Jews say that the Arab countries told them to leave until the war was over and Israel was destroyed. Those Arabs, who now call themselves Palestinians, went to Jordan but were thrown out after behaving poorly, and went to other Arab countries which also didn't accept them but kept them in refugee camps for propaganda purposes. Most of the Jews were absorbed into Israel. Anyway, your question is a good one but was done 65 years ago. Israel is now a full fledged country, and the UN cannot simply send its citizens elsewhere, anymore than you'd tolerate them deciding that the US should be relocated to the Antarctic. I did my best to remove my personal views from this explanation, and to just answer your core question.
Jews have a great love for Israel because its their home. Israel is the birthplace of their nation, bible, ancestors, and contains the resting/worship area of G-d (the Temple, Jerusalem).
That's the area of the world that now primarily comprises parts of Israel.
It depends on who you mean by "the Arabs". If you are referring to Arab citizens of any state, even Israel, then most Arab land-holdings are in the Galilee region in the north of Israel, although there is a significant Arab population with land-holdings in Haifa, Acre, and Jerusalem. If you are referring to Arab governments, the Arabs own no territory in the State of Israel. Hamas controls the Gaza Strip and the Palestinian Authority controls parts of the West Bank, neither of which are in sovereign Israeli territory.
There was no Israel in the Roman world. The area that is present day Israel was called Iudaea or Judaea by the Romans. It literally means "the country of the Jews".
Palestine
Palestine
Israel was created for the Jews so they could have a homeland after the Holocaust. Palestine was under mandate by the British who encouraged the creation of the homeland to be carved out of Palestinian land. This area had been occupied by the Jews in ancient times.
Your question is wrong. Israel creation occurred in British areas. this areas was never Arabic. The act was not malicious towards the Arabs. The area where the Land of Israel (the biblically defined region) was had no Arabs at the point in time when the Israelite Kingdoms reigned since the Arabs at the time were living almost exclusively in the Arabian Peninsula. During the Rise of Islam period, over 1000 years later, Arab armies and populations resettled the "Northern Middle East" which consists of places like Iraq, Syria, Lebanon, Jordan, Israel, and Palestine. These Arabs interbred with the local peoples and Arabized them (this is a cultural/identity process). Therefore, the Land of Israel became host to an Arab population. When Jews made a political gambit to get the Land of Israel back, it now had an Arab population that could trace its roots back for at least 800 years and considered the territory part of their birthright. If the question is asking, why did the Jews not choose Patagonia or some other region with no discernible native population, the answer is the same reason as why the Kurds and Circassians also do not want a State in their Diasporas. There is something intrinsic about all of these people and their connection to the place of their origin. Jews have the right to not have to compromise their historical identity for momentary peace.