Joined means that they have registered but not yet installed the Dropbox desktop application.
Completed means that your friend has successfully installed the Dropbox desktop application and both of you have been credited your bonus space (huzzah!).
Ineligible means that the recipient is ineligible for the referral program. Either they have already registered an account with Dropbox or are attempting to register using the same computer as you. These restrictions are intended to prevent people from gaming the system (cheating). If you feel this status is inaccurate or applied unfairly, double-check the email address of your recipient and try again.