At the moment, when you complete a quest in World of Warcraft and get rewarded with some gear, only the items your character can use get added to your cosmetic wardrobe, where all your transmog options are stored. This means if you're a leather user, your plate-wearing alts won't get any goodies, aside from maybe a cloak. This tyrannical system is coming to an end in The War Within.
This system was teased when Blizzard announced Warbands, which unifies your characters by sharing some reputations and item appearances.