1. What does it mean?
An abbreviation of 많은 관심 부탁드립니다, literally asking for plenty of interest. It is a breezy sign-off for an announcement, a new project, an event, or a piece of creative work.
2. The nuance
The full expression is polite, but the abbreviation makes it casual and promotional. It asks people to pay attention; it does not specifically mean 'please buy' or 'please donate.' Use the full phrase when a formal tone matters.
3. Examples
“주말에 작은 전시를 열어요. 많관부!”
I'm holding a small exhibition this weekend. Please come check it out!
“첫 영상 올렸어. 많관부, 그리고 의견도 환영해.”
I uploaded my first video. Show it some love—and feedback is welcome too.
Sources
Korea Housing Finance Corporation: Korean slang guide
References support the meaning and usage. Example sentences are written for NoCapWiki.