In the S08E02 of Game of Thrones, Bran says that the Night King will come for him and that the Night King hunted down many three-eyed ravens.
Sam: Why? What does he want?
Bran: An endless night. He wants to erase this world and I am its memory.
I never noticed, but does Bran mean he is literally the world's memory? If he dies, everyone will forget everything?
What Bran is referring to is his ability to use greensight to see the past, something he has been able to do at will since inheriting the role of Three-Eyed Raven. For example, he was able to look back and see Jon's true lineage. Bran seems to imply that this ability is unique to the Three-Eyed Raven -
He'll come for me. He's tried before, many times, with many Three-Eyed Ravens.
This could also serve as an explanation for Bran's purpose as the Three-Eyed Raven, to be "the world's memory." Samwell also comments on the importance of Bran's ability -
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 you.
So, the answer is no, the world will not literally forget everything. However, there will be no one left who can "remember" everything.
It could very well be, and we might find out soon enough.
In the second episode of the eighth season, Sam Tarly tells Bran that
“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 you.”
More to the point, in the conversation with Jaime Lannister, responding to the Kingslayer's question what happens after the battle, Bran asks him:
“How do you know there is an afterwards?”
This Time article delves deeper into the role of Bran in the light of the episode, summarising his role regarding the Night King with this paragraph:
Bran’s job as the Three-Eyed Raven is to remember (and see) all of history — not a biased version that men write in history books, but the actual truth. By destroying Bran, the Night King essentially would destroy the very history that sustains man and helps him to evolve.
Perhaps worth noting that Bran isn't the only one to claim to be the world's memory. When speaking about the Citadel, Archmaester Ebrose tells Sam in no uncertain terms "we are this world's memory". Making this statement doesn't mean that everyone would succumb to amnesia if the Citadel fell, but that a great repository of the history of men would be lost. Bran holds the ability to see the world's entire history, so losing him would be losing the memory of many things.
I think we're collectively forgetting season 6, where Bran learns of his powers. His use of "greensight" is demonstrably more than passive. Bran has [limited] ability to change history.
I have no reasoned theory why or how he can do this but I do think it's fair to say that the Three-Eyed Raven is a lot more than just a living diary. The way he can interact with people in their past suggests he may be omnipresent through time. He might even be time itself.
If you wanted to everlasting winter, Bran looks like a good target. Killing time, or turning time are both pretty effective routes. I don't think we have enough knowledge of the White Walkers at this point to determine their actul aims. I look forward to it.
If you want to bring ruin to the world of man, and keep it that way, you're going to want to prevent any survivors from simply rebuilding. So you'd burn down libraries and Citadels and what have you so people can't simply pick up a book and (partially) resume civilization where it left off. This has in fact been done several times in the history of our own world. One could argue it is essentially what was done with slaves in the US. When you conquer a people you want to integrate them into your empire (or whatever you call it) and prevent them from rising up against you. Destroying their world and culture and replacing it with your own is a simple way to ensure this.
The (Three-Eyed) Raven is the ultimate end-run around that: given enough time he could rattle off entire histories, traditions, technologies, etc. and enable a rapid rebuilding of the world of man.
As such, if the Night King desires to throw the world of man into a ruin from which it may never recover, he must somehow prevent The Raven from undoing it all.
The following are some things to consider...
As a point of interest, the untitled Prequel 'Age of Heroes'/'Long Night' TV series (in development/Pilot filming this summer) synopsis states,
"Taking place thousands of years before the events of Game of Thrones, the series chronicles the world’s descent from the golden Age of Heroes into its darkest hour. From the horrifying secrets of Westeros’s history to the true origin of the White Walkers, the mysteries of the East to the Starks of legend, only one thing is for sure: It’s not the story we think we know."
So we have to consider how important is it that Bran knows everything vs who he tells what things too, meaning, "what good is it, if Bran knows things, but doesn't actually tell certain people the whole truth?", because essentially all of Westoros is built on lies!
Another thing to consider is that after the "Hodor Paradox" combined with what the previous Three-Eyed Raven told Bran about "The Past is already written. The ink is dry" it seems that we are in a predetermined universe in a cycle cosmology [ghost] story. Well at least until we break into a new cycle, then who knows, maybe free will becomes more possible?
But if so, if they are in a predetermined universe, then even Bran's actions are "moot" because he's just fulfilling his destiny, as opposed to having any real power to change anything and therefor everything he says, is not necessarily the exact truth, as much as that is what he needs to say for other characters to fulfill their roles of destiny too! (ie: if they think Bran is important, then they will be compelled to do "a, b, and c".)
And one last thing to consider, is if Bran is the world's memory, what good is it, if he ends up either dying before TNK or being the only survivor? Now I'm doubtful that Bran being the only survivor will happen, but as a possible scenario it calls into question his statement, unless time travel is involved for Bran and he gets stuck in the past, but even then, unless he can make an alternate reality, it seems moot -- still just doing what he has already done.
