Seriously. wow.
You could hit up the wiki page for the conflict for an overall highlight reel.
Without going into too much detail.
late 1800's Jews in Europe started the "Zionist" movement to find a safe homeland for the Jews as persecution throughout Europe and Russia was rampant. While they focused on many areas throughout the world in Africa and even Philadelphia, the finally focused on ancient Israel by WWI due to circumstances after the war when the Ottoman Empire was beginning to decline and the area of Palestine (as well as all Arab lands) were under control of various European countries, specifically Britain in this case.
During WWII Britain made agreements with Arab leaders and promised sovereignty to any nation that fought with them against the Ottoman's where Arabs were a majority. This happened in every nation except what was then called the Palestinian Mandate. In fact Britain later contradicted their earlier agreements and created a White Paper that said they would support a Jewish homeland (not state) in the area.
When the war ended in 1945, wealthy European Jews began to legally purchase large farming lands that were owned by Arabs who didn't even live there but were being tilled by local Palestinians for centuries. Once the Jews owned the land they made the Palestinians leave and began a huge push for what was then illegal immigration of many Jewish Europeans to Palestine to run these farms or Kibbutz.The immigration was illegal as a Britain was not allowed to have any shift populations under the mandate, however, due to well formed Jewish militants (first terrorists of the region, Stern Gang and Irgun), Britain was virtually unable to stop this immigration of not only people but also large caches of weapons.
Between 1945 and 1948, as a result of this combination of legal land purchases and illegal immigration, the Jewish population of Palestine skyrocketed from 10% to just over 40%. On top of that they were nearly all European with strong military training and a modern supply of weapons. Whereas Christian/Muslim Palestinian population were farmers, having never been in the world wars, and if they had any weapons, they were largely inferior and outdated Ottoman rifles.
In 1947-8, the Zionists were successful in pushing the UN to vote in favor of a separation of the land in Palestine where Jews received about 45% of the land, however, it was 78% of the land that was capable of being farmed. Clearly an unfair separation of land that shouldn't have even been up for sale in the first place as of the portion that was being given to the European Jews only about 20% of that was even legally owned by Jews.
So, in 1948 Israel was created against the cries from Arab leaders, Jews throughout the Arab world fled the now rampant attacks in Arab lands to Israel (first time Jews in Arab lands were really mistreated), and the first succession of wars between a far larger and more capable Israeli military vs a largely divested Arab army that has always had outdated equipment.
From then until 1967 there were a few wars where either Israeli leaders were clearly trying to grow by force or Arab leaders were trying to kill them off. In reality the Arab leaders were also trying to grow by force as they never had any intentions of creating a Palestinian state either. However, by 1967 words were flying again, but it was clear that no Arab force was going to dispel Israel as they struck all their Arab neighbors in what would now be called a pre-emptive strike and immediately decimated the air forces of everyone and in six days were able to easily take Golan Heights, Gaza, Sinai, and what is now the West Bank. Shortly after Egypt was able to strike a deal to get Sinai back due to US negotiations. However, the other lands have been occupied since.
Forward nearly 50 years and you have a Arab populace that has almost only known the very harsh and often brutal standards of life living under constant gunpoint and settler attacks as well as dehumanization and they have grown incredibly hateful, vengeful, and mostly only want to see Jews die. However, the leadership is divided and those in WB want to see a Palestinian state in the now occupied territories, while those in Gaza state openly the only condition they accept is no Israel. However, any logical person would know they would eventually accept a Palestinian state and removal of violence if it were to happen and be accepted by the populace.
While the Israeli side has also grown very weary of this long conflict as most of their population have grown up under nearly constant attacks from suicide bombers and other bloody attacks from the various Palestinian militant groups. They also have a large amount of hate and distrust towards their clear enemy. Their leadership has historically demonstrated the want to eventually only keep all of the lands and the settlement movement was intended to create these facts on the ground, however more recently they've shown a possibility to return a great portion of it based on certain other conditions and even halted settlement expansion temporarily. (btw, keeping any of the land is against international laws and Israel has been committing great crimes by not leaving decades ago, thank you US for supporting state terrorism)
Now, they are discussing, again, the way forward. They need to solve a few issues.
1. Right of return for Palestinian refugees to their homes that are inside Israel. This will undoubtely be given up by Palestinians in trade for some other compensation.
2. Future of Jerusalem as both parties hold claims of future capitol. Not really sure on what will happen here. Its way too complex from every angle and point of view. Maybe the only solution would be if it was internationalized and became its own state that was ruled by UN and others, idk.
3. Where exactly the lines will be drawn. Palestinians want it back to the 1967 borders (which were already far away from the original lines of 1948). However, Israel since then has built many illegal settlements that now house tens of thousands of Jews. So, more than likely the large settlements relatively close to the 1967 border will be annexed by Israel and rest will go to Palestine.
4. Future state of security and relationship. This is hard as there is no trust between them and both sides contain very strong extremist groups that always try to attack the other.
One sign of hope is that Obama has been far more even handed than any previous administration, at least in front of cameras, and the Arab nations as a united voice years ago said they woudl accept fully peace and full normal relations with Israel if they moved back to the 1967 borders. Basically this shows that they would do the same if a Palestinian State were to be created and Israeli occupation ended.
Now I left out a TON of little wars and "terrorist" actions from both sides of the camp to just stop on the highlights and big parts of the story. But, this should give you a basic idea of what's going on.