The Dragon Banner is the banner of Lews Therin Telamon, also known as the Dragon. It has a picture of a rippling dragon on it. It is described as being neither woven nor sewn together nor painted, but all of one piece.
The Dragon Banner may in fact be a ter'angreal of some sort or have some other connection to the Horn of Valere; the Heroes summoned by the Horn seemed to consider it important, and it was found along with the Horn. It is possible that the Heroes will follow the one who holds the Dragon Banner, or that they will only follow the Dragon into battle; in either case, they appeared to refuse to enter battle until the Banner was properly flown.