The data you can enter through the Coursera “profile”, while it is not compulsory, promises potential career opportunities, new connections and course recommendations. This may be of less interest to those who have an existing level of education, a job and existing connections; however, if you are visiting Coursera with the hope of increased career opportunities, it may be significant (although it is difficult to tell without further analysis or Coursera data).
In addition to the site activity data (presumably course searches, enrolments and so on) collected by Coursera, the additional information you can provide to personalise your ‘learning experience’ and recommendations is fairly extensive, including work experience, education, career goals, location, age and gender:
There do not seem to be any options (easily visible on this page, at least) for hiding all your data from everyone else (including Coursera staff, ‘Content Providers’ and ‘business partners’), nor do there appear to be any options for customising who can view your site activity. For an educational site – where some may be following a promise of improved career opportunities, and where everyone is not beginning at the same ‘starting point’ – it, in my opinion, seems appropriate to be able to hide all data from everyone.