"Though heavier and slower than their one-handed counterparts, two-handed swords offer an advantage that is readily apparent – they have a large bladed area, which makes them frighteningly lethal."— Game Guide(src)
While they existed before Diablo III, they were classified along with one-handed Swords. In game, they are mostly used by Crusaders, and Demon Hunters are the only class to never use them. Interestingly, there are no crafted legendary heavy swords. Note that Two-Handed Swords may not be transmogrified into any other weapon type.
Some of the Two-Handed Mighty Weapons are shaped as two-handed swords.