Konak is a generic term for any residence of public official. In this case, it was the residence of the Ottoman governor of Sofia. I am not sure what kind of administrative unit Sofia was the centre of, but anyway it was a major town of 30 thousand inhabitants (a lot at that time). The Sofia Konak was also used as a court of law. The 1873 trial of Vassil Levsky, the Bulgarian national hero, was held there.