There's really a lot to it; a very complex answer. The Mandate of Palestine (as the area was called under British rule) was partitioned and portions ceded to Israel. The Palestinians, who had been there for centuries under Ottoman rule were told after World War 1 that the Mandate was made in order for the Palestinians to have their own nation, saw this as their homes being "given" to Non-Palestinian/Jewish settlers. They rejected the UN partition and "forced" Israel into a war of independence. The Palestinians, for reasons historians have a hard time agreeing on, fled the Holy Land. One reason was fear after the Deir Yassin massacre, by direct orders from the Zionist forces or psychological warfare. The problem wasn't so much then, but when the dust settled and these refugees wanted to come home to their homes. Israel so far hasn't granted universal right to return to the Palestinians and has actually passed legislation blocking those refugees from returning and claiming their property. Imagine if you fled from a civil war and when you tried to come home the people who won said you couldn't come home nor have any of your stuff: that's what happened here. The reasons are really political in nature and will make this discussion quite contentious if you try to pick a side, but needless to say, innocent people have been negatively affected with generations of Palestinians still living as refugees of a war that ended 60+ years ago. That's one reason.

The other reason is Israel illegally (per International law ) establishing settlements in The West Bank. The West Bank was supposed to be established as a Palestinian state, but it was occupied by the Israeli army during the Six-Day War and they haven't ceded complete control since.

There are lots of reasons really, these are just a couple, but the big thing to remember is no matter who "started it" so to speak, neither side is truly behaving in a respectable manner. The Palestinians have turned to Hamas and terrorism to push their side and Israel is ignoring the Palestinian claims and keep on trying to expand their borders.

Disclaimer: I hope I came off as impartial in this. I have a particular side and opinion, but this entire conflict has created emotions that run deep all around the world. I would hope that this discussion stays as unbiased as possible because there is two definitive sides to this story.