What do tutors look for during an oxbridge interview?

Interview sturctures differ widely, but most of them consist broadly of three elements: 

1. A question to break the ice, for example why you choose to study the subject. However, some interviewers may skip this question or simply ask who you are or where you are from to break the ice. 

2. Questions about your subject that you are not expected to know the answer for. The aim of these kinds of questions is to see how you think and how you appraoch unfamilliar material. 

3. Questions to assess your critical academical thinking in the subject. This may include unseen passageses you have to comment on (critically) or (in sciences) problems you have to comment on. 

Often, there is no correct or incorrect answer, and your wat of thinking is more important than your answer. A tutor once told me he personally looks for candidates he thinks will be happy in their subject, so passion and ability to think independenlty (thrive in the independent study environement of oxbridge) were crucial for him. However, again, it all varies per interveiwer.