The Prime Minister of the Republic of Korea (국무총리 / 國務總理, Gungmuchongni) is appointed by the President of South Korea, with the National Assembly's approval. The officeholder is not required to be a member of the National Assembly. The Prime Minister is not the head of government but is similar to that of a vice president.
The Sino-Korean word gungmu (국무/國務) means "state affairs" and chongni (총리/總理) means "prime minister", "premier" or "chancellor", so the full title in Korean means literally "Prime Minister for State Affairs", but it is not used as official English title. The short title in Korean is just Chongni.