It is anonymous to some extent. Managers receive an aggregate data of the feedback from their team, but who individually provided what feedback is not shared. This is done so that they can take action from the feedback received.
If you and you're manager have worked together for some time, he's probably familiar with your writing style. So if you write comments in the free form fields, those can give them clues as to who wrote something, since managers might have some sense of who the disgruntled employee is versus who might be happy.