What are they: This term is used to distinguish non-nuclear weapons from nuclear ones.
What it means: Of course it doesn't mean that because weapons are 'conventional' they are somehow more acceptable or less lethal. In the 'conventional' raid by Allied planes on Dresden in February 1945, as many civilian people were killed as in the nuclear attack on Hiroshima in August 1945. It took a thousand bombers and tens of thousands of bombs to destroy Dresden. Just one bomber aircraft and one bomb devastated Hiroshima - but creating the bomb had involved thousands of people behind the scenes. In fact, nuclear weapons have not been used since 1945, but at least 20 million people have been killed in wars fought with conventional weapons since then.
Think about it: Isn't it misleading to think of weapons as if they can be categorised as more or less harmful? They have one function: to kill. Some do it rather more horribly (such as cluster bombs or chemical weapons) or comprehensively (such as firebombs or nuclear weapons) than others, that's all. At the receiving end, people are maimed and killed, and in that sense the weapon doesn't matter. People were shocked to hear that the US forces in Iraq had used napalm, which was used to set fire to forests (and people) in Vietnam, and is on the international list of banned weapons. It was certainly another troubling reminder that in war anything goes. But what is more shocking is that weapons are used against citizens at all.