1. What does it mean?
강추 shortens 강력 추천, a strong recommendation. In reviews and conversation it gives a compact, enthusiastic endorsement of something the speaker thinks others would appreciate.
Also written or said as 강력 추천, 강추하다
2. The nuance
It states an opinion, not a guarantee that everyone will like the same thing. Adding who it suits makes it more useful: a quiet cafe can be 강추 for reading but unsuitable for a large gathering. It says nothing by itself about sponsorship.
3. Examples
“조용히 책 읽을 카페를 찾으면 여기 강추야.”
If you want a quiet cafe to read in, I highly recommend this one.
“지도 없이 걷기 좋은 짧은 코스라 초보 여행자에게 강추해.”
It's a short route that's easy to follow without a map, so I really recommend it to new travelers.
Sources
KoreanClass101: Korean language lessons
References support the meaning and usage. Example sentences are written for NoCapWiki.