Elrond’s story about his father is a mostly accurate, if short, summary of what Tolkien wrote about Eärendil. He didn’t go “single-handedly,” because his wife Elwing went with him (which is a whole story in itself). And the light seen as the evening star in Middle-earth is one of the Silmarils, which Eärendil wears as a headpiece. The Silmarils are jewels which shone with the Light of Valinor, but which can’t be mentioned by name in The Rings of Power because Amazon don’t have the rights to The Silmarillion.
Eärendil is Elrond’s father, and also Aragorn’s ancestor through Elrond’s twin brother Elros (yes, Aragorn and Arwen are distantly related). Eärendil was the son of a Man (Tuor) and an Elf (Idril) while his wife Elwing was the grand-daughter of a Man (Beren) and an Elf (Lúthien), so Elrond and Elros have both Elf and mortal ancestry on both sides. Their father Eärendil was known as “the Mariner” and built his own ship with help from the Elf Círdan the Shipwright.
After their bravery in the war against Morgoth, Eärendil and Elwing, along with all their descendants, were given the opportunity to choose whether they wanted to live as Elves or as mortals. Both chose the Elves, but of their sons, Elrond chose the Elves while Elros chose to become mortal, and became the first King of Númenor – we saw his picture in a tapestry in episode 3. This is why Arwen has to choose between going with the Elves or staying with Aragorn and becoming mortal in The Return of the King.
Bilbo sings a song about Eärendil while the hobbits are staying at Rivendell in The Lord of the Rings (including a reference to the Silmaril) so it’s possible we’ll hear more about him over the course of The Rings of Power, since that puts it in the category of material from The Lord of the Rings, i.e. material Amazon is legally allowed to adapt. In the meantime, it’s clear that the legacy of his famous father hangs over Elrond’s head. The Rings of Power has chosen to really play up the tension between Men and Elves, and Elrond’s Half-Elven status is something he carries almost as a burden, while his separation from his family – as both parents are in Valinor and therefore unreachable, and his brother is long dead – is also something that leaves him feeling rather lonely and outcast.
That problem may eventually be solved by Galadriel, since he will ultimately end up married to her daughter. However, since Galadriel doesn’t appear to have any children yet and we haven’t heard so much as a whisper of her husband Celeborn, he may have to wait a while. (In Tolkien’s mythology, Galadriel and Celeborn are married but living separately at this point. Whether that’s the case in the show has yet to be revealed as Celeborn hasn’t been mentioned at all).
Unlike Elrond, Galadriel is all Elf, and in fact she is a grand-daughter of one of the very first Elves created. She has been referred to several times as “daughter of Finarfin” in The Rings of Power, but the show hasn’t gone into any detail about what that means, probably because Finarfin is barely mentioned in the Appendices to The Lord of the Rings, which means Amazon don’t have the rights to his story.