After revision: the paper is not anonymized - what does it mean? I finally got the revision of my paper, but one of the reviewers complained that the paper is not anonymized. Since I'm not the native english speaker, it's quite strange to me. 

Does it mean that I should remove authors names from the paper? If so - what for, and why should I do this?
To add to @Brian's answer, in double blind review besides submitting your manuscript without author names, you should eliminate any information about datasets, affiliation or previous works that may betray your identity. E.g. for an Elsevier journal here instructions for double blind review to authors say:


  Besides the obvious need to remove names and affiliations under the
  title within the manuscript, there are other steps that need to be
  taken to ensure the manuscript is correctly prepared for double-blind
  peer review.  To assist with this process the key items that need to
  be observed are as follows:
  
  
  Use the third person to refer to work the Authors have previously undertaken, e.g. replace any phrases like “as we have shown before”
  with “… has been shown before [Anonymous, 2007]”. 
  Make sure figures do not contain any affiliation related identifier 
  Do not eliminate essential self-references or other references but limit self-references only to papers that are relevant for those
  reviewing the submitted paper.
  Cite papers published by the Author in the text as follows:  ‘[Anonymous, 2007]’.  For blinding in the reference list:  ‘[Anonymous
  2007] Details omitted for double-blind reviewing.’
  Remove references to funding sources
  Do not include acknowledgments
  Name your files with care and ensure document properties are also anonymized.
  


Of course, this hiding of information is limited only during the review rounds and after your work gets accepted, the camera ready copy of the publication should include all the relevant information , that was hidden / anonymized during the review rounds.