Here's a quick attempt, which is open to revision and criticism:
The British had a mandate from the League of Nations in the twenties to administer over the territory of Palestine, formerly Ottoman Turkish Empire property, in order to create a national home for the Jews.
In 1948, a UN resolution split Palestine into two territories, one for Jews and one for Palestinian Arabs. The Arabs revolted against this, losing the war, and with it their claim to/control over the territory they had been allotted (most of which ended in Israel and Jordan). Many Arabs ended up relocating to the Gaza Strip and the West Bank.
In 1967, the Six Day War saw Egypt attack Israel, followed by hostilities between Israel and Jordan. When the smoke cleared, Israel had control of much of the West Bank and Gaza Strip, and over time Jewish settlements were built in these "occupied" areas.
"Occupied" is in quotes because that's what much of the fuss is about, as to whether the settlers are actually entitled to be there and to whom that land really belongs. Are the Arabs entitled to the 1948-era Palestinian state, the West Bank and Gaza Strip, or no state at all? Other nations have ventured into these hostile waters tentatively, if at all.
The Oslo agreements reduced the hostilities to a dull roar for a while in the mid-90's, but the rise of Ariel Sharon in Israel stirred things up again, as both Sharon and Arafat have shown little hesitation towards poking each other with a stick.
(My source for the above: <a href="http://www.mideastweb.org/mpalestine.htm">mideastweb.org</a>, after a quick Google search. I make no claims as to its bias or authenticity.)
Okay, NOW throw Judaism vs. Islam into the mix...