Here's my take on it; I read a couple of academic tomes on the matter some 10 years ago but things have changed even since then, and I've forgotten a lot as well.
Firstly, some people feel that the Jews have some kind of biblical right to return, as they were exiled from the kingdom of Judea (roughly, Jerusalem) nearly 3000 years ago, and the Jews are God's Chosen people or something like this. Now, you can see this is the first place where the issue becomes slightly fraught, as many people don't really care what the bible says and this is a matter of debate even among biblical scholars.
The Zionist (returning Jews to Israel) movement took hold roughly around the 1900's, and then of course WW2 and the Holocaust gave it even greater traction. I think this is the second part where there's a lot of disagreement, because many people rightfully point out that the Holocaust was a European atrocity that demanded a European solution (rather than forcing the Palestinians to give up their homes, why not the Germans?). I believe that Uganda was considered as an option for a while.
Then Israel was created in 1948, and Jews began immigrating according to a schedule laid out by its's creators (more or less, the Brits).
Tension naturally erupted and then there was the war of 1967, when the Israelis captured greater chunks of the region i.e West Bank and Gaza Strip, and this is where the real problems began; most of the international community views these gains as illegal.
Israel has since continued to illegally settle on Palestinian land; the UN has more censures against Israel than ANY OTHER NATION owing to its illegal settlements.
In addition to this, they left the Palestinians with relatively little water and are notorious for their blockades that prevent Palestinians from carrying on with normal life - i.e. getting to hospitals or developing businesses properly.
Lastly, the Israeli army is subsidized by the US, which is at least partly owing the HUGE Israeli lobby in the US. This of course creates a David and Goliath situation, Palestine is one of the poorest "countries" in world and they're effectively reduced to throwing rocks in the mighty Israeli army, as well as the very well publicized suicide bombings. The occupation has undoubtably radicalized the Muslims in the region because of the perceived wholesale robbery of land rights.
I'm obviously pro-Palestinian and this is ungoogled so anyone should feel free to correct my facts.