Yeah, that's about it in a nut shell. that's all you will need to know to understand most conversations around the water cooler.
The deeper truth and understanding about this current conflict and it's roots will take much more reading and research on your part.
As it relates to the Gaza strip and the West Bank as well, you need to understand that Israel wants these lands and other parcels of land it currently does not occupy to become part of Israel proper. If you accept this principal as a truism much of what has transpired there in the past twenty years can be understood easily.
You see, Israel has tried to make life unbearable for it's indegious Arab population hoping that they would leave on mass to nieghbouring Arab countries as had happened in it's early years as a country circa 1945-1950. Menachem Begin,
once Prime Minister of Israel was a founding member of the
Irgun (considered by historians as the world's first example of a terrorist group) used common thuggary and threats to scare
many Palestians off their lands. Many of these Palestinians still reside in Jordan, Egypt, Syria, Lebannon and other Arab countries.
Currently, peace between Syria and Israel is possible but only if Israel returns the Golan Heights to Syria. But it will do no such thing, they want the land. In 1982 Israel annexed a large part of Southern Lebannon in order they said to stop PLO terror attacks, but they really just wanted the land. Hezbollah finnally forced their removal in 2000 in all of Lebannon except for a very small parcel of farm land.
Over the past three years a very large wall has been built through the West Bank in order to stop terror attacks Israel says. But they really just want the land that has been annexed by the wall's contruction. As for the Gaza strip,
there was a truce in place that expired about a month ago.
The truce bound Hamas to not launching any rocket attacks into Israel. In turn Israel was bound to loosing up the border crossings which in turn allows the free movement of goods and people from Gaza into Israel which in turn helps the economy of Gaza. You see, although Israel removed it's settlements and military from Gaza according to the Oslo Accords in 2005, Israel still maintains control over air space, territorial waters, offshore maritime access, the population registry, entry of foreigners, imports and exports as well as the tax system. However, when the truce date expiried it was clear that Israel did not hold up it's end of the bargain. Talks to extend the truce were not successful then Hamas launched it's rockets abscent any truce. Then Israel has now launched it's current offensive and Bush says it's all the fault of Hamas? Well what would you expect from a guy who tells you Sadam has WMD's then sends in our military so his friends in the MIC can make some coin.
Hope that clears things up a bit.