Weapons of slaying kill a specific class of monster in one hit. They are also guaranteed to hit that monster. For example, if you equip a spear of animal slaying any toad you attack will perish in one hit.
A weapon of jelly slaying does not get corroded when attacking an acidic jelly. This does not protect it from other creatures which corrode weapons, however.
A weapon of slaying will "gleam balefully" if equipped in the presence of a monster it targets.