What is the vernacular?
The term vernacular simply means the mother tongue of some country or region -- it is the language most spoken in that area.
I assume that you are asking this in regard to the Divine Comedy because this book was actually written in the vernacular. Since Dante was writing in Florence, the vernacular was Italian.
This is a big deal because, in those days, almost all writing was done in Latin. The Church used Latin, scholars used Latin, it was the lingua franca of the civilized world (or at least Europe).
So when Dante wrote in Italian, he was helping to establish it as a serious language that could be used in literature.