WARNING: The following contains spoilers for My Hero Academia Season 5, Episode 3, "Clash! Class A vs. Class B!", now streaming on Crunchyroll, Funimation and Hulu.
Episode 3 of My Hero Academia's fifth season begins with Deku reflecting on his bizarre dream, wherein he had a conversation with All for One's brother, the first user of One for All. In this dream, the first user shows Deku memories of the past; specifically, the beginning of the long-running feud between One for All and All for One. Deku, only being able to use 20% of his Quirk, cannot learn more about his predecessors as the first user explains that his connection to them is not yet strong enough. This implies that when Deku gains more control over his Quirk, the first user will properly tell his story.
Deku then discusses these events with All Might, hoping for some insight from his mentor, but unfortunately, All Might is just as surprised that the first user can speak to Deku directly. Even All Might's predecessor, Nana Shimura, did not have this ability, so All Might theorizes that this is a trait unique only to Deku. Much of Deku's experiences with One for All are unique to him -- All Might and Nana never experienced or knew about in great detail. For example, All Might could control One for All immediately after receiving it, unlike Deku, who is still training to unlock 100% without damaging his body.
The main reason for this is that One for All is a Quirk cultivated with each user, growing stronger as it's passed down. In Season 2, Episode 20, "Listen Up!! A Tale from the Past," All Might explains that One for All was initially a very weak Quirk, hence the first user's decision to pass it down, allowing it to grow stronger so it could one day rival All for One's tyranny. This means that Deku possesses the most powerful version of One for All to date.
This peculiarity grants Deku many new opportunities that his predecessors did not have. Firstly, having access to the first user's memories will help him better understand All for One's goals and how he came to be. As an extension, he might understand Shigaraki better since both are successors of One for All and All for One, respectively. Right now, Deku has very little information of the legacy that was thrust upon him so suddenly, but gaining different perspectives could give him a better outlook and the means to finally put an end to All for One for good.
Overall, the vestiges seem to have a similar role as Avatar Roku had to Aang in Avatar: The Last Airbender, able to pass on wisdom from their own unique experiences to better Deku as the ninth holder, though more challenging to access. Already having a solid determination to become a great hero and fulfill his role as a One for All successor, Deku will soon come to have the advantage of taking care of his long-term goals.