What does data partition in nandroid backup contain?
I think that the best answer is here.  As an Android Expert, I couldn't have said it better myself!


  To my knowledge, TWRP does a nandroid backup. As you can read in the
  tag wikis of the mentioned tags (nandroid, backup), a Nandroid backup
  takes images of your partitions. It's not a backup on the file level,
  but on partition level. So it includes everything stored on those
  partitions. Doing a full Nandroid backup of your system thus includes
  the entire system, one file per partition. There are only very few
  things not contained, such as the radio-firmware.
  
  So to put it as a short direct answer to your question: Yes, a full
  Nandroid backup would include all your apps, app data, messages,
  contacts.
  
  Though it might be complicated to extract them separately (Nandroid
  can't do that, it's always an "all-or-nothing". But e.g. Titanium
  Backup can read data from Nandroid backups. Just in case you'll need
  that :)