Zones are areas of the map with designated themes, mobs, and scenery.
These areas have borders much like a state or country, and though invisible, they define areas. They may contain subzones, cities, towns, villages, or instances.
For example, the zone of Dun Morogh contains the subzone of Coldridge Valley, the city Ironforge, the town Kharanos, and the instance Gnomeregan.
In lore and the official website, a zone is usually referred to as a "region" (however, the community has basically forced Blizzard to start using zone instead).
Furthermore, lore regions and in-game zones do not always match up (what may be a region in lore may be reduced to a subzone in-game, or some subregions may become their own zones).