Named after revered Syrian/Palestinian arch-terrorist Shaikh Ezzedeen Al-Qassam* (b. 1820, d. 1935), Qassams are primitive short-ranged rockets, developed and home-made by Hamas terrorists. They are used exclusively and extensively against civilian targets in Israel.
All Qassams are fuelled by a solid mixture of sugar and potassium nitrate (the latter is also used in suicide bombings), and carry a TNT/urea nitrate mixture inside the warhead. The first two Qassam models (Qassam 1 and Qassam 2) could carry 0.5kg and 7kg of explosives, respectively; The Qassam 3's used today carry up to 20kg each, and are the only ones that have killed Israelis. Some Palestinians were killed by all Qassam models, in what Israeli media likes to call "work accidents".
The Qassam 3's extended range (10 kilometers) allows Hamas to attack the city of Sderot almost daily, and it has become their main target. Sderot had been clumsily bombarded with Qassams for months before the statistically inevitable happened and a Qassam hit someone on the head. Then it happened again. And again. And it's still happening. Sderot, by the way, is not a settlement on occupied land, but part of Israel proper. Its existence is as legitimate as Tel Aviv's (and that, come to think about it, is probably why Hamas and others wish for its destruction).
The IDF is currently operating in Gaza in another attempt to stop the Qassam launchers, who operate mostly from homes, schools and the like. Most of the rest of the world, predictable and hypocritical as always, rushed to condemn Israel's defensive actions as soon as they began. Not a word about the Qassam death toll, though.
* Hamas' official military wing (not that there is much of a distinction between terrorist and non-terrorist Hamas activity these days) is called "the Ezzedeen Al-Qassam Brigades", after the same guy. They have a propaganda website at http://www.alqassam.info/english/ including a (wholly biased) biography of Shaikh Al Qassam.
Sources: The Internet and my personal knowledge.
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