Basically, the region currently known as Israel was Palestine before about 1920. The people who lived there were called Palestinians.
After World War One, Britain and France divvied up the Middle East, and Britain got a Mandate over Palestine. This worked fine, apart from the occasional riot/protest for independence, until after World War Two, when Jews who survived the Holocaust needed somewhere to be resettled. There had long been talk of the Jews founding their own nation to escape the anti-Semitic vibes around Europe from about the late 1800s, this was known as Zionism. Two places ended up being nominated, through a buy-out of land, not hostile takeover. The first was Palestine, as it sat around the traditional holy sights of Judaism, and was the original home of the Jews. The second was Argentina, but that never amounted to much.
So after the Second World War, the UN decided the Jews needed a home. So they created the "Partition Plan." This basically meant they evacuated the majority of the Palestinian population from Palestine in order to allow the Jews to establish their own nation, Israel. This angered the Palestinians and the surrounding Arab nations, and basically the area has been in constant conflict ever since. The basic theme up until recently has been the Arab nations warmongering, but Israel eventually surviving.
This conflict now is about a territorial dispute between Israel and the Palestinians, and I think it's Israel on the offensive. Basically, the Palestinians are feeling the effects of the current conflict a little bit more than the Israelis.
Hope it helps.