1. What does it mean?
베프 is a shortened Korean rendering of English 'best friend.' It refers affectionately to a very close friend and is common in relaxed conversation and personal captions.
Also written or said as 베스트 프렌드, best friend
2. The nuance
The word does not require an exclusive ranking of friends. Someone may talk about several 베프, and using the label publicly does not oblige the other person to describe the relationship the same way. 절친 is a close Korean alternative.
3. Examples
“베프랑 매년 같은 날에 만나서 사진을 찍어.”
My best friend and I meet on the same day every year to take a photo.
“새 도시로 이사했지만 베프와는 매주 통화해.”
I moved to a new city, but I still call my best friend every week.
Sources
KoreanClass101: Korean language lessons
References support the meaning and usage. Example sentences are written for NoCapWiki.