Posted from the US
Israel's war with the Hezbollah factions based in Lebanon can be summarized in the following way:
Israel: Leave us the hell alone!
This was not a war about winning - this was a war to make the point that Israel was done sitting back and letting Hezbollah fire rockets from its cradle in Lebanon at Israeli cities and people. This war also made clear to the Lebanese that if they allow the Hezbollah to have safe harbor in their midst, hiding behind women, children, and the eldery - that eventually all of them would pay the price. They paid a heavy price. The lesson to Lebanese:
Don't allow terrorists to breed among you and instigate a country which is tired of being attacked by terrorists. Be accountable for your country and disarm those who have an agenda misaligned with the national interest.
Israel said: enough is enough.
Lebanon is not an innocent bystander - they let a terrorist army breed and arm within its borders with full knowledge of the Lebanese government. They allowed the Hezbollah to attack a neighbor who would not attack them but for the instigation of this terrorist army. The Lebanese let this happen. They have a government and an army who could stop the Hezbollah and they did nothing.
To completely destroy Hezbollah, Israel would need to destroy a lot more of Lebanon - which was not the point. The hope is now that the Lebanese and the UN and whatever multinational force is required will create a buffer zone and stop Hezbollah from acting in a way which harms both Israel and Lebanon - this is a viral group which attacks others and brings harm to its host.
Here's a secret ingredient for peace in the Middle East: leave Israel alone. Guess what - do that and they will leave their Arab neighbors alone - which would be a great start. Since 1948 Israel's Arab neighbors have had one endless war with the country, with a new proxy fighting each time. It has all been a total waste of lives, energy, and resources. The latest conflict was a summary of all the others - radicals on a senseless mission (let's destroy Israel because we want to) leading to destruction and death all around. Peace will occur when fanciful dreams of destroying and antagonizing Israel become replaced with healthy dreams of being good neighbors, economic partners, and focusing on building the health and wealth of the region.
Israelis do not live the the abstract war that many in the US understand. The US attacked, invaded, and largely destroyed many parts of Afghanistan and Iraq to chase down terrorists. What would the US do if terrorists lived across the border and had daily suicide bomb attacks from the south and rocket attacks from the north? The reaction would be terrible, swift, and massive - US citizens would never tolerate what the average Israeli tolerates.
If you irritate a lion it will bite hard - and no one should be suprised when it does.