Challenge Mode came out during the Mist of Pandaria (MoP) expansion in which player´s gear scale to a certain ilvl and they had to complete dungeons at heroic level. The goal was to complete the entire dungeon in a certain time, and depending on how long it took to complete the dungeon, they were rewarded with gold, silver or bronze.
Completing all dungeons in Challenge Mode with gold status, rewards transmog gear. In Mist of Pandaria it was an entire set except back and weapons. In WoD, the rewards are weapons.
Challenge Mode gear has always been locked to the player that got the achievement. When Legion comes out, if you have completed the Challenge Mode WoD dungoens (during WoD exp), you can buy a token that unlocks the Challenge Mode weapons and make them account-wide.
Not stated yet how the MoP gear will turn out yet.
Also, at the moment it seems that you will only get the sets of the class you've already got them on.
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