Hi Felix,
For the affiliation field, yes, putting the university you're studying at is a perfectly good answer.
Note that you can browse public data on CoralNet without signing up. On the other hand, note that signing up doesn't enable you to just add annotations to any source (project) yourself, unless you get the source owner's permission first.
Typically you would sign up if you A) have some benthic images to upload and do analysis with, or B) are in contact with someone who has some data on CoralNet already. So, that's why we generally assume that you do have a project to describe.
Hope that makes sense, and let me know if any other clarification would be helpful.