The horn of an animal is a symbol of its power to defend itself. To raise up here is to bring into existence or to enable to act. The Messiah is spoken of as if he were a horn with the power to save Israel. AT: "He has brought to us someone with the power to save us" (See: [[rc://en/ta/man/translate/figs-metaphor]])
David's "house" here represents his family, specifically, his descendants. AT: "in the family of his servant David" or "who is a descendant of his servant David" (See: [[rc://en/ta/man/translate/figs-metonymy]])