So, what the hell is Bran's "destiny" all about?
Bran was called/lured North by "the three eyed-crow" (the last greenseer).
In the books he meets a mysterious possibly "undead" man, who the black hands but doesn't have the blue eyes, though. He is also intelligent, contrary to the other wights so far. He guides them over the Wall and further north until they reach a protected area where the 3 eyed-crow/seer and children of the forest are. Bran starts learning about his powers, and has some interesting dreams.
That's where the books stopped at for now, so I doubt we'll reach this point this season. This is more likely the arc they'll develop for Bran next season (along with Jojen getting weaker and weaker, and a relationship between Meera and Bran developing), with him reaching the cavern near the end of the season.
The undead (Coldhands) appears to have been cut altogether (they might introduce him next year, if he has a role beyond ADWD, but for his first arc he was cut). He was supposed to appear at the Nightfort in last year's finale, guide them under the Wall, make Sam promise not to tell anyone Bran is alive etc. then lead the kids to destination.
If I'm wrong and they intend to show more than new, maybe more revealing, visions from the 3 eyed-crow as Bran continues North, it might be a Child of the Forest he meets in episode 10, and there's a fight against Wights to get in.