1. What does it mean?
남친 shortens 남자친구. In its usual conversational sense it refers to a romantic male partner, not just a friend who happens to be male.
Also written or said as 남자친구, namchin
2. The nuance
For a platonic male friend, 남사친 or 남자인 친구 is clearer. 남친 does not by itself tell you anything about the gender of the person who has the boyfriend.
3. Examples
“남친이랑 주말에 서로 좋아하는 영화를 한 편씩 보기로 했어.”
My boyfriend and I agreed to watch one favorite film each this weekend.
“옆에 있는 사람은 남친이 아니라 오래된 동창이야.”
The person next to me isn't my boyfriend; he's an old classmate.
Sources
References support the meaning and usage. Example sentences are written for NoCapWiki.