At long last, the Night King's army is knocking on Wintefell's door on Game of Thrones, and that means we're in for a major battle. Jon Snow and his companions are ready for the undead king — or at least they think they are thanks to a plan partially hatched by Bran. The reigning Three-Eyed Raven explains that he's the perfect bait to get to the Night King and end his reign once and for all, so he'll be waiting for his foe in the Godswood at Winterfell. It seems the leader of the White Walkers wants to erase mankind's memory (the Three-Eyed Raven) by killing Bran before he spreads an endless night to across the Seven Kingdoms. That poses a powerful question: what if the Night King succeeds in killing Bran? Would that doom the world or would his death be more symbolic?
We know that there's been a Three-Eyed Raven even longer than there's been a Night King. In fact, the Night King is made by the Children of the Forest, who seemingly work alongside this powerful figure who knows everything that has ever happened. The previous Three-Eyed Raven trains Bran for the sacred position, but Bran hasn't had an opportunity to prepare a successor in the event that he dies. It feels safe to say that the position will die with him if he falls in the Godswood, but the exact meaning of his death remains unclear.
Symbolically, it would leave the world without a safety net. As Sam points out while the plan is being formulated, "That's what death is, isn't it? Forgetting, and being forgotten. If we forget where we've been and what we've done, we're not men anymore. We're just animals. Your memories don't come from books. Your stories aren't just stories. If I wanted to erase the world of men, I'd start with Bran." The implication is there are parts of humanity that will be lost forever if Bran dies. Things like the Night King's creation, the truth about the First Men and where they come from, the full extent of magic in Westeros . . . all of these things will fade from the memory of mankind over time without a Three-Eyed Raven to carry the knowledge for the world.
Still, there are other ways to record history. Sam and Tyrion are prime examples of people who know the value of books and memories. They know that knowledge is more powerful and enduring than swords, and while that's not the same as having an encyclopedic memory of every event that's ever happened, it's a promise that as long as there are people who keep an account of all the great stories, they'll never truly die. If there's never another Three-Eyed Raven, it will be a tragedy. The world will permanently lose a bit of its mythos and magic, but unless there's something more to the story that Bran hasn't revealed, his death alone won't doom Westeros. But it will damage the morale of all those fighting for the survival of humanity.
To put it another way, Bran wouldn't offer himself up as bait if there's no hope for the world without him in it. He knows way too much for that. He may very well die, creating a world existing without a Three-Eyed Raven for the first time ever, but his death alone won't win the war for the Night King. It could feel like the beginning of the end for all those he leaves behind, though.