The dead king? At the age of 210 years.
Not half elf, but a bit elven blood in his veins 🙂 He's the very far heir of Elros, the brother of Elrond, who was a real half-elf (as Elrond also is) but chose mortal life, while Elrond preferred living as an elf (all this lies back in the First Age about 6500 years before the War of the Ring)
Eowyn is talking about the Dúnedain; these are the heirs of the former Kings of Arnor, the Lost Kingdom. It was founded shortly after Gondor by Elendil and his sons Anárion and Isildur (well, rather Isildur; Anárion stayed in Gondor).
About 1000 years before the War of the Ring, Arnor was broken after several attacks of the armies of the Witchking; afterwards, only few survived and lived in the woods, called the "Rangers" or the "Dúnedain", and the heirs of the son of the Last King Arvedui of Arnor were the Lords of the Dúnedain - Aragorn was the last of them and reunited the kingdoms of Gondor and Arnor and was king in both.
(strange how often the word "last" occurs is this post 😄 😄 and even more if I would add that Elendil was the son of the last of the Lords of Andúnie in Númenor and one of the few who survived the drowning of Númenor and came to middle-earth................)