"The chest presents the widest, easiest target for attacks against the human body; unfortunately, several vital organs also happen located there. Torso protection tends to be heavy as a result."— Game Guide(src)
Body Armor (a.k.a. Torso or Chest Armor) in the Diablo series refers to protective items worn on the chest. In all three games, Body Armor determines the way the character looks, including transmogrification in Diablo III. It usually provides higher protection than items on other slots.
Body Armor could be any thing from Cape to Gothic Plate. Armor is equipped to improve your Defense rating. Armor usually has high durability, but also high Requirements for Strength. Light armors include everything from Rags to Studded Leather Armor. Medium armors include mails from Ring Mail to Splint Mail. Heavy armors are metal plates ranging from Breast Plate to Full Plate Mail. The appearance of a character changes depending on which armor type you are equipping.
There are many types of body armor, each with its own unique look, for every class, and each with a combination of the three types for every limb. The three types are light, medium, and heavy. Some armor sets look similar with only about one difference between them (e.g. Scale Mail and Ring mail look almost exactly the same, except that the left and right arms of scale mail have the medium appearance while the ring mail arms have the light appearance). The armor progressively gets better, but heavier armor also causes running to drain more Stamina.
Armor may have up to four Sockets.
In addition to common stats, Body Armor may roll resistances, reduced damage from elites / melee / ranged attacks, increased damage of tertiary skills, Life %, Life regeneration, Thorns, Life per Kill, health / gold pickup range, and up to three Sockets. Offensive stats may only roll on Legendary and Set Body Armor.
While Body Armor is no longer a single highest protection slot, it is still a vital part of character's gear, most importantly due to the ability to customize it through the highest number of sockets among all items.