Armor is the general term in the Diablo series for items worn on the body, mainly for protection. In fact, all equippable items except Rings, Amulets and Weapons are classified as Armor for gameplay purposes. Most types of Armor items increase the character's Defense (off-hand non-Shield items may or may not, but still count as Armor).
Armor may also refer to Chest Armor, Body Armor or Torso Armor, the type of items worn on the character's chest: i.e. breastplates, cloaks, capes, chain mails and other types of torso protection.
In addition, mutually-exclusive Sorceress Spells (Frozen Armor, Shiver Armor and Chilling Armor), Druid Cyclone Armor and Wizard conjuration spells (Ice Armor, Storm Armor and Energy Armor) are commonly known as Armors.
Armor got several additions: Belts, Circlets, Boots, Gloves and class-specific items, which are variants of regular armor: Barbarian Helms, Druid Pelts, Paladin Shields and Necromancer Shrunken Heads.
Diablo III added three more armor slots: Pauldrons, Pants and Bracers, as well as many class-specific variants of existing Armor types: Cloaks, Quivers, Crusader Shields, Mighty Belts, Spirit Stones, Voodoo Masks and Wizard Hats. In addition, for Socketing purposes, all items (including off-hand items) except Helms and Weapons count as Armor.