For the most part, all committed data gets stored in the p directory. The write-ahead logs (w and zw) can also store mutations at points in time before being committed and moved to the p directory. In case Dgraph crashes, the write ahead logs can be replayed back.
The files in each directory are specific to Badger. The data is both stored in the vlog and sst files. Feel free to file a GitHub issue to Badger about adding more documentation about the vlog, sst, and MANIFEST file.