Gaza is a densely populated strip of land that is mostly surrounded by Israel and peopled almost exclusively by Palestinians. Israel used to have a military presence, but withdrew unilaterally in 2005. It’s currently under Israeli blockade.
The sporadic rocket fire that’s hit Israel from there since its pullback has strengthened Israeli hawks’ political position, as they have long argued that any Palestinian state would end up serving as a launching pad for attacks on Israel.
Egypt controlled Gaza until 1967, when Israel occupied it (along with the West Bank) in the Six-Day War. Until 2005, Israeli military authorities controlled Gaza in the same way they control the West Bank, and Jews were permitted to settle there. In 2005, then–Israeli Prime Minister Ariel Sharon pulled out Israeli troops and settlers unilaterally.
Gaza is governed by the Islamist group Hamas, which formed in 1987 as a militant “resistance” group against Israel and won political power in a 2006 US-based election. Hamas’s takeover of Gaza prompted an Israeli blockade of the flow of commercial goods into Gaza, on the grounds that Hamas could use those goods to make weapons to be used against Israel. Israel has eased the blockade over time, but the cutoff of basic supplies like fuel still does significant humanitarian harm by cutting off access to electricity, food, and medicine.
Hamas and other Gaza-based militants have fired thousands of rockets from the territory at Israeli targets. Israel has launched a number of military operations in Gaza, including an air campaign and ground invasion in late 2008 and early 2009, a major bombing campaign in 2012, and another air/ground assault in the summer of 2014.