남기다 is the transitive of 남다: deliberately leave something behind. Online it is the word for posting — 이렇게 남겨주시면 감사하겠습니다 'I'd be grateful if you left one', 리뷰 좋게 남길게요 'I'll leave a good review'. It also covers capturing something (영상으로 이렇게 남기는 게 처음 'the first time it's been captured on video like this'), leaving a legacy (크게 남긴 업적 'any great achievement left behind'), and leaving length: 윗머리는 조금 길게 남겨주세요 is what you say to a hairdresser.