Theodred is King Theoden's son and Prince of Rohan. His mother died at his birth in the year 2978; after that Theoden never took another wife.
After his sister's death he "adopted" his niece, Eowyn, and his nephew Eomer.
Theodred died in the first battle against Saruman's Orcs on February 25 in the year 3019.
With his death the line of the Kings of Rohan was crossed and Eomer, who was the closest relative, became King.
Theodred was twenty-five back then. In the "Book of Lost Tale" we learn more about his friendship to Eomer.