mwa ha ha ha! okay step one DON'T LISTEN TO MINDSPELL!
basically, a zillion years ago the Jews came to the area of Israel and settled it, driving out the previous inhabitants, who later died out. (I don't think they were even Arabs, but some other ethnic group). eventually the Jews got driven out by still unrelated ethnic groups. at some point the driving-outs ended, the land became under occupation by the Romans, Ottomans, British, etc., and the Jewish and Arab inhabitants had to live under those conditions without an independent state. (the reason I go into this is to explain that nobody living there now has a "more legitimate" claim to the land than anyone else).
so, the 20th century comes and both the Arabs and Jews are doing independence movement stuff. both of them have their moderates, their militias, and their extremist groups who set off bombs and stuff. finally the British are like "Time to go!" and withdraw in 1948.
they draw up a plan to partition the land into two areas--one for each ethnicity. The Palestinians get the lion's share, but the Jews say Yes anyway. The Palestinians are unwilling to give ANY land to the Jews, so they say No.
So a war breaks out, and six Arab armies invade to figt alongside the Palestinians, and the Jews somehow kick everyone else's ass, and end up with a lot more than the original agreement. The Palestinians say "Okay, now we accept the agreement" and the Jews are like "Too late, dudes". A lot of Palestinians have fled to the West Bank and Gaza Strip during (which remain Palestinian--the West Bank is part of Jordan at this point) the fighting and lost their homes and stuff.
behind the scenes, the Arab leaders of repressive states around Israel (Syria, Egypt, to some degree Jordan, Iraq, etc.) see the Palestinians as a great opportunity, so they make them a huge cause to refocus their publics' ire away from their own evilness, so they do all this stuff to keep the Palestinians dispossessed and stateless (like supporting violent terrorism on the part of Palestinians, knowing it will lead to Israeli military responses...or keeping shitty, crime- and terror-ridden "refugee camps" full of Palestinians in their territories and not granting them citizenship...or turning the public against any Arab leader who suggests a moderate, peaceful solution and calling them a Zionist...etc.)
1967 comes around, and Egypt, Syria, and Transjordan attack again. (Syria is basically the behind-the-scenes mastermind and tricks Egypt into starting the war by closing Israel's ports, and strong-arms Jordan into joining the battle against its wishes). Israel beats them all up again. partway through the war Jordan attacks from the West Bank, precipitating an Israeli invasion; the Jordanians retreat and Israel now owns the West Bank. Jordan is seriously sick of the Palestinians and is pretty glad to get rid of it.
so here's the whole occupation thing, and what's going on today: Israel decides that it's going to occupy Gaza and the West Bank (and the Sinai and the Golan Heights and some other places) and trade them for peace. if the Arab states will recognize Israel and stop declaring war on it, they get the land. some right-wing Jews, however, think the land is OURS FROM GOD and do NOT want to trade it for peace.
so, decades pass, the Arab states won't trade land for peace (why would they? it's in their best interests to keep the Palestinians oppressed and stateless and Israel the villain), and Israel starts settling the occupied lands, driven by those right-wing religious Jews.
finally (today) Israel decides enough is enough and pulls all its settlers out of Gaza--all troops, too, leaving the territory entirely in the hands of the Palestinians. the hazy idea is that perhaps one day the West Bank will be the same, perhaps if a non-terror-fueled, modern democratic Palestine emerges in Gaza. of course, the evil right-wingers don't intend to pull out of the West Bank ever and see this as an opportunity to finalize a shitty, tiny Palestinian state.
who knows if it will work out. Hamas has a ton of power in Gaza and may end up with a leadership role, which is problematic because their charter denies Israel the right to exist at all, which is (to say the least) not conducive to peace. the challenge is promoting a moderate, secular Palestinian leadership that believes in a two-state solution, i guess.
there. questions? inaccuracies?