Since your other question was about quantitative and qualitative sociology, I will relate this one to that one. Microsociology is a particular kind of qualitative sociology. It is a type of sociology that seeks to understand the interactions between individuals and society or individuals and other individuals. In terms of the perspectives on sociology, microsociology fits especially well with symbolic interactionism.
In microsociology, researchers look at the smallest units of society. That is, they look at individuals and how they interact with one another. They seek to understand what these interactions can tell us about broader sociological forces. What this means is that microsociology tends to overlap with other disciplines such as psychology and anthropology, both of which can be much more interested in individuals and their thinking than more macro approaches to sociology are.
So, microsociology is an approach to understanding society that requires qualitative research done on the smallest units of society. It does not try to look at large social institutions and phenomena. Instead, it looks at the interactions between individual people.