Your fit interview will most likely have a distinct theme - e.g., Leadership, Personal Impact, Entrepreneurship, etc.
For each of these themes, interviewers will be looking at a variety of factors. For example, if the question is on Leadership, the interviewer will want to assess why was this an important experience for you, implying what Leadership truly means to you? How did you manage any pushback or conflict? What was the impact of your action? What did you learn from this experience that helped you grow as a Leader? Is there anything you would have done differently?
Keep in mind, the situation does not always have to be professional in setting. One of my interviewees had a great story on how he showed Leadership as a rock climber in a competiton, and he ended up getting an offer. Just want to lay it out because people try to over index on professional stories at the expense of lesser depth.
Hope this helps!