Interviews are required for all students- and are critical for admission. Think of it as a series of gates- once you have the standardized test scores you are through that gate. Same with the admissions test, your personal statement and your recs. If you get invited to interview you are seen as a viable candidate- so then it’s how you do in the interview (the other things only come back into play if you are a ‘maybe’ after interview). From what I understand Cambridge interviews a higher % of applicants than Oxford (they admit at about the same rate, so it’s just when they do the bigger cut)
The interviews are done by supervisors (professors) in the subject that you are applying to study, not admissions people. It varies a bit by subject, but you will be given problems to solve, asked about relevant concepts, etc. You may be asked readings or ideas that you have mentioned in your PS (I do know somebody whose interviewer was the author of a book that he had talked about in his PS!). Some of the material will feel familiar, but you should expect to be given unfamiliar / more advanced material as well. Then you bring together everything you do know and try to work it out. The supervisors will ask you questions which usually contain hints. The goal is to see how you think, how you approach unfamiliar material, and how you are likely to do in a tutorial learning format (it genuinely doesn’t suit everybody). There is minimal chat.
Oxford will interview by Skype if you can’t get over, but Cambridge is just dipping it’s toes in the water- last I heard there was at least one college that has used them, but don’t count on it. Otherwise, you get yourself over there. Interviews are in early December and you hear in late November.
People have wildly different views of their interviews. I know people who came out crying thinking that they tanked (and one who cried in the interview) who got offers and people who came out confident and didn’t. I know people for whom it was excruciating but quite a lot for whom it was kind of fun (once they settled into it anyway- nobody likes the anticipation!).
Look on YouTube for some great videos.