1. What does it mean?
Short for 남자 사람 친구, 남사친 distinguishes a male friend from 남자친구, which ordinarily means a boyfriend. The extra 사람 makes the platonic meaning explicit.
Also written or said as 남자 사람 친구, namsachin
2. The nuance
It describes the relationship being presented, not proof about anyone's hidden feelings. There is no need to assume every friendship is a possible romance. In a context where gender is irrelevant, 친구 is often enough.
3. Examples
“같이 사진 찍은 사람은 동아리 남사친이야.”
The person in the photo with me is a male friend from my club.
“남사친한테 생일 선물로 줄 책을 골랐어.”
I picked out a book as a birthday present for a male friend.
Sources
KoreanClass101: Korean language lessons
References support the meaning and usage. Example sentences are written for NoCapWiki.