Warning! SPOILERS for Foundation episode 4
Salvor Hardin is clearly the hero destined to save Terminus in Foundation, and episode 4 revealed she possesses abilities that bind her to the Vault. When Hari Seldon's colonists arrived on the planet Terminus to establish their Foundation, they quickly realized everything was not as they had expected. They discovered a mysteriously barriered artifact called the Vault, which didn't show up on scans and proved inimical to life. It generates a powerful null field that affects anyone or anything that gets too close.
There is, however, one exception: Salvor Hardin, who had been conceived on the journey through the stars. The colonists consider Hardin an "outlier," a person who couldn't possibly have been factored into Seldon's predictions for the Foundation, and thus they largely reject her. None of them are quite comfortable enough to question whether the potential existence of outliers means Seldon's predictions are flawed, but Seldon herself lives in fear of the possibility she could unwittingly doom the galaxy. Still, with the Anacreons arriving on the Foundation and the first Seldon Crisis finally beginning, she is being forced to step up and demonstrate some pretty unusual abilities. Some of these suggest that, far from being an outlier, in reality Hardin is the key to Seldon's plans.
There appears to be a strange bond between Hardin and the Vault, perhaps a result of Salvor being exposed to cosmic radiation when she was still a fetus. She is uniquely resistant to the Vault's null field, something she uses to her advantage against the Anacreons in Foundation episode 4, and Salvor has begun receiving visions - hallucinations that have served to guide her and expose the Anacreons. The Vault was created by Seldon himself in the original Isaac Asimov novels and short stories, and presumably the same is true in Foundation. That means Salvor is receiving guidance from some sort of sophisticated system left behind by Hari, helping her navigate the Seldon Crisis. One vision in Foundation episode 4 sees her briefly experience Hari Seldon's old library on Trantor, perhaps indicating she will soon receive a direct recorded message.
Curiously, Salvor Hardin appears to possess preternatural instincts and a remarkable predictive ability. She is almost empathic in her ability to read others, again perhaps coming from the Vault, given the bond she has with it must be psychic in nature. What's more, as Salvor demonstrates to a captive Anacreon, she is able to correctly predict the tossing of a coin with 100 percent accuracy, a feat that should be almost impossible. It's reasonable to assume this, too, is a power somehow tied to the Vault; although how it works is unclear at this point.
The Salvor Hardin of Foundation is very different to Isaac Asimov's books and short stories. Asimov's version is a male academic who is famous for calling violence the last refuge of the incompetent, whereas Foundation's is very much a woman of action. All these powers and abilities are original as well, meaning it will be fascinating to see where Foundation takes its version of Salvor.