Basically Jews started arriving in what was once Palestine in the late 19th century due to rising antisemitism in Europe (there were already Jews living there before that but a small number). Following the Holocaust there was a huge displacement of Jews many of whom sought to go to the Holy Land. In 1948 the UN partioned Palestine with 80% going to the Arabs (which is now Jordan) and including Jerusalem and 20% to the Jews in what is now named Israel. Obviously some people living there were displaced and a lot of the surrounding Arab nations joined forces to eliminate Israel altogether in what became known as the War of Independence.
During this time there were a group of people who Israel's creation displaced but were never really accepted by Jordan either. They became known as Palestinians. At the time numbering around 600k(but now well over a million)
Over the next few years there were a number of wars and skirmishes culminating in the 1967 war where once again all the Arab nations including Jordan, Lebanon and Egypt went to war with Israel (who knows who really started?). Over the years and particularly in this war Israel (despite being massively outnumbered) captured the Golan heights, Sinai and Jerusalem. Some of which has since been handed back as peace treaties. However, as the holy city Jerusalem was never up for debate. during this time many of the Arab nations expelled 850k Jewish residents many of whom moved to Israel.
Over the next 60 years there have been continuing wars. In the 90s with Rabin as PM they very nearly came to peace terms but Rabin was assassinated and the peace treaty never got signed. Israel offered many a peace treaty over the years including large swathes of land but they have never been accepted by the Pal governments who to be fair to them understandably wanted the land back of their displaced citizens and refused for anything less than all of Israel.
the last major peace treaty Israel offered was in the late 90s and kicked off what was called the 2nd intifada. This including Pal suicide bombings in Israel mainly aimed at civilian populations including school buses and pizza palours. The Israeli government came down hard and built walls and check points with the areas of large Pal communities (ie Gaza and the West Bank). However, following some negotiations they agreed to pull troops out Gaza in 2004. Hamas was duely as the government from then on (whether it was legally and fairly elected is a matter for debate) and they haven't had another election since. They were meant to have an election this month but its suddenly been cancelled (make of that what you will).
However, Israel has continued to build settlements in the West Bank to accommodate their ever growing population. This is illegal under UN law and has caused even more resentment as more and more Pals have been displaced.
Every few months there are skirmishes between the two areas usually with Hamas firing rockets (Israel says they hide rockets and weapons in civilians centres and during the last war there was international recognition that a hospital that was bombed was bombed from the inside by a faulty rocket so there is some truth to it). Israel invested heavily in a defensive capability called the iron dome which anilates the rockets in the air so they don't to too much damage though do occasionally get through and people are killed. Every so often Israel , fed up with all the rockets, then hits the nuclear option and goes on an offensive into Gaza/west bank and bomb the crap out of them.
Eventually Hamas surrenders because they run out of rockets, Israel starts building again and a few months/years later the whole thing starts again.