1. What does it mean?
막콘 abbreviates 마지막 콘서트. It refers to the last performance within the concert schedule being discussed, whether a local multi-day run, a tour leg, or the full tour.
Also written or said as makkon
2. The nuance
It does not necessarily mean the artist's last-ever concert. Establish which set of dates someone is talking about before reading permanent finality into it.
3. Examples
“서울 공연은 막콘만 갈 수 있어.”
Of the Seoul shows, I can only attend the final one.
“막콘 멘트가 기억에 남아서 후기를 적었어.”
The closing-night remarks stayed with me, so I wrote up my impressions.
Sources
References support the meaning and usage. Example sentences are written for NoCapWiki.