1. What does it mean?
여친 shortens 여자친구. It usually means a romantic female partner rather than any female friend.
Also written or said as 여자친구, yeochin
2. The nuance
여사친 or 여자인 친구 makes a platonic relationship clearer. The shorthand is common in casual speech, but 여자친구 may suit a more formal introduction.
3. Examples
“여친이 만든 도자기 컵을 사무실에서 쓰고 있어.”
I use a pottery cup my girlfriend made at the office.
“여친 생일 선물은 본인이 갖고 싶다고 한 걸로 골랐어.”
For my girlfriend's birthday, I chose something she'd said she wanted.
Sources
References support the meaning and usage. Example sentences are written for NoCapWiki.