Geoffrey Batchen defines vernacular photography like this:
The term ‘vernacular’ literally means the ordinary and ubiquitous but it also refers to qualities specific to particular regions or cultures. Its attachment to the word ‘photography’ allows historians like myself to argue for the need to devise a way of representing photography’s history that can incorporate all its many manifestations and functions. A vernacular history of photography will have to be able to deal with the kind of hybrid objects I describe above, but also with, for example, photographies from outside Europe and the U.S. It may mean having to adopt non-traditional voices and narrative structures. It will certainly mean abandoning art history’s evaluation system (based on masterpieces and masters, originality and innovation, and so on). In short, the term ‘vernacular photography’ is intended as a provocation and a challenge.
There’s also this post on the subject from juniorbonner.
A lot of the time the term ‘vernacular photography’ also seems to be synonymous with ‘found‘ photographs – particularly old, faded, crumpled photographs found lost or abandoned in a shoebox at a garage sale – someone else’s memories, with their technical and aesthetic ‘flaws’ left bare, their subjects left unidentified, and their narratives subject to the inventions of imaginative or curious viewers.