What is the meaning of not being able to pray the mincha in a place that has received Shabbat in advance?

Shalom, Thank you for your question. As you probably know, a person or community is able to accept "early Shabbat" on Friday afternoon (from "plag hamincha" time). Even a shule that does not have an early minyan, will often bring Shabbat in a few minuets before the last possible time, so as to merit "tosefet Shabbat", that is adding to the Shabbat from the weekday. In any event, once a Shule has bought Shabbat in by the minyan in shule, by saying Lecha Dodi (for example), then an individual is not allowed to pray the weekday mincha inside that shule. They must go outside the synagogue and pray there (see Shulchan Aruch, 263,15). The reason for this law is that it is inappropriate that a weekday prayer be said in the place that has bought Shabat in, as it looks like a "desecration" of the holiness of the Shabbat. Blessings.