Israel left Gaza and began pulling out of the West Bank in 2005. Palestinians gave power to a radical group that began firing rockets at Israel. Egypt and Israel decided to blockade the region to prevent the group from getting supplies used to obtain weapons.
Hamas continually fires rockets at Israel. Rockets that do very little. The rockets don't pose a real threat to Israeli life. With an advanced rocket defense system and the low tech nature of the attacks, maybe 1 or 2 people will be killed in a month of rocket fire. Of course, any life lost is a tragedy, but it's clear that these attacks aren't going to take down Israel, or do much real damage. They're provocation.
They're provocation because Palestinians dying is good for Hamas. It increases hatred of Israel, and that hatred is what they use to rally people in support of them. It makes Israel look like murderers in the eyes of the international community (which may be fair since they are uhhhh you know murdering people) which they can use to apply international pressure for Israel to give into demands.
After about a week of bombing Egypt tried to broker peace between the two sides. Israel accepted and stopped firing. Hamas continued to fire rockets that would do absolutely nothing except provoke further attacks, and they made DEMANDS. How on Earth can a state with no real military strength make demands? What leverage do they have? The only leverage is their own dead citizens. They fire rockets from civilian locations, their leaders hide among civilians, and they hide rockets in schools (particularly in UN schools that were built to provide sanctuary to civilians).
Of course, Israel has a choice not to target these areas. These rockets don't produce much real human damage, and sparing hundreds of Palestinian civilians may only mean one of two casualties. Israel's policy seems to be that they are willing to kill dozens of Paletinians to save an Israeli life which is a stance I'm not sure I agree with.
However, whatever you want to say about Israel, you have to agree with this. Israel is a country whose primary interest is in the well being of its citizens. Unfortunately, the same cannot be said about Hamas. If and when a government rises to power in Palestinian that truly is looking out for their citizens, the war will end as it does not serve anyone's best interests.