Presumably they're using a FileWriter because they want to write to a file. Both BufferedWriter and PrintWriter have to be given another writer to write to - you need some eventual destination.
(Personally I don't like FileWriter as it doesn't let you specify the encoding. I prefer to use FileOutputStream wrapped in an OutputStreamWriter, but that's a different matter.)
BufferedWriter is used for buffering, as you say - although it doesn't buffer all the output, just a fixed amount of it (the size of the buffer). It creates "chunkier" writes to the underlying writer.
As for the use of PrintWriter - well, that exposes some extra methods such as println. Personally I dislike it as it swallows exceptions (you have to check explicitly with checkError, which still doesn't give the details and which I don't think I've ever seen used), but again it depends on what you're doing. The PrintWriter is passed the BufferedWriter as its destination.
So the code below the section you've shown will presumably write to the PrintWriter, which will write to the BufferedWriter, which will (when its buffer is full, or it's flushed or closed) write to the FileWriter, which will in turn convert the character data into bytes on disk.