The Order of the Dragon is an order of knights originally founded by Tiber Septim. Throughout the Empire's history, there have been only six previous champions of this order.
You become a member and the seventh champion of this faction upon completing the Main Quest, specifically at stage 60 of the quest Light the Dragonfires. According to High Chancellor Ocato, you are bestowed "the highest rank possible in the Order of the Dragon". However, the faction only has one in-game rank, Champion of Cyrodiil. You are the only character in Oblivion who can join this faction, and membership grants you access to the Imperial Armory and a full set of Imperial Dragon Armor. Imperial Guards will treat you respectfully due to your position. For more information, see the faction entry.