내려오다 is coming down, and after -아/어 it does two jobs. Physically: 한참 뛰어 내려오셔 'he's running all the way down', 돌음계단을 따라 내려오는 샹들리에 'a chandelier coming down along the spiral staircase'. Figuratively — and this is the more useful one — passing down through time: 전해 내려오다 and 전해져 내려오다 'be handed down', used of legends and proverbs, and 이어 내려오다 'be carried on', used of family businesses and old customs.
Register: neutral; slightly formal in the handed-down sense