1. What does it mean?
A playful expression for two people who are getting romantically close but have not established that they are a couple. It overlaps with 썸, the uncertain stage where there seems to be mutual interest.
Also written or said as 삼귀는
2. The nuance
This is a joking description, not a fixed relationship category or proof that both people feel the same way. It is better used about your own situation than to announce someone else's relationship for them.
3. Examples
“우리 아직 사귀는 건 아니야. 삼귀는 중이라고 할까?”
We're not officially together yet. Maybe you could say we're in the almost-dating stage?
“친구들이 삼귀냐고 물었지만, 나는 아직 잘 모르겠어.”
My friends asked if we were almost dating, but I'm not sure yet.
Sources
Korean Institute for Healthy Family: communication teaching resource
References support the meaning and usage. Example sentences are written for NoCapWiki.