For much the same reasons as there is trouble in Northern Ireland - 2 peoples who think the land should be all theirs. the Israelis see it as their ancestral land promised them in Genesis (c. 2000BC), but after Jerusalem was sacked in the 1st Century AD, very few of them actually lived there. The Arabs moved in over the next few centuries and it was only in late 19th/early 20th centuries that the Zionist movement seriously tried to repopulate it with Jews. After the Second World War, the Jewish people were understandably keen to establish a homeland of their own and so successfully kicked the British out of British Mandated Palestine (as was) and (re-)established the state of Israel. The surrounding Arab states didn't take too kindly to it and refused to recognise the state, but since every time they've tried to invade the Israelis have given them a bloody nose and taken another slice of their territory, they have in practice accepted the state (though except for Eygpt, they still don't officially recognise it as a sate). The Palestinians are essentially the people who've been dispossessed by Israel's expansion.