Gaza was under the British control after the the collapse of the Ottoman Empire. When Egypt attacked Israel in May 1948, they overran the area. Cairo started the All-Palestine Government but ruled the territory as a protectorate. This ended in 1967 when Egypt attacked Israel again and lost. Israel took control of Gaza at that point. Israel was not too happy abobut inheriting this poor, heavily populated and hostile territory.
Since 1948, Egypt has received $1.8 billion a year from the USA. They could just absorb Gaza and thus earn this money.
The 1.3 million Gazans speak a colloquial Arabic exactly like the Egyptians of Sinai. They have more family ties to Egypt than to the West Bank where Fatah resides. They are more economically tied to Egypt. Hamas terrorists came from the Egyptian organization, The Muslim Brethren. They really are not "Palestinians" anymore, but are called that to be politically correct.
The intifada began in 1987. That brought about the Oslo accords of 1993. In 1994 went to Yasir Arafat's Fatah that was promising to bring stability and prosperity to Gaza. However, in 2006 the radical terrorists, Hamas, won in elections and controlled Gaza. Fatah joined them. Israel pulled out completely then. Fatah launched rockets into Israel in 2002, hitting Israel's Sderot constantly along with other neighboring towns.
Condoleeza Rice warned Israel not to retaliate to rocket firing, so Olmert tried some economic hardships to cause Hamas to lose favor with the population. On January 17 the Israelis escalated by cutting fuel and closing the borders because the attacks were getting much worse. The press has put pressure on Israel to stop, and they have. All this has happened because of Israel pulling out of Gaza and giving in to the demands of others.
Daniel Pipes suggests that the Gazans are incapable of self rule and Egypt should take it over again. I think he has a great idea.