Leather armor is generally worn by rogues, druids and monks throughout their full WoW "career", as well as by hunters and shamans while they are below level 40. Leather armor provides more protection than cloth armor, but less than mail or plate armor. At level 40 both hunters and shamans are able to wear mail armor. Warriors, paladins, and death knights can wear leather, but usually choose not to, due to its lower armor value than mail and plate, also most leather gear does not come with +Strength, which is more desirable to plate wearing classes because stacks with buffs such as Mark of the Wild or Blessing of Kings, while pure attack power does not. However, a Warrior or Paladin specced for DPS or healing may choose to use Leather Armor if the stats are an improvement in damage or healing; as a tanking class will be taking most of the damage in a group, the high mitigation provided by plate armor may not be necessary for a DPS or healer.
If an armor is leather in-game it will be tagged with "leather". Leather armor can be crafted by the Leatherworking profession.