I am struggling to understand why would I want to use MultipartFormDataStreamProvider when I can get all the information using HttpContext.Current.
It is much easier to
This is what I found on MSDN. I think this might help you.
The stream provider looks at the Content-Disposition header field and determines an output Stream based on the presence of a filename parameter. If a filename parameter is present in the Content-Disposition header field then the body part is written to a FileStream, otherwise it is written to a MemoryStream. This makes it convenient to process MIME Multipart HTML Form data which is a combination of form data and file content.