This can be a really hard question to answer - I often found it quite uncomfortable because you're essentially bigging yourself up!
It's an inherently personal question, so it's really hard to suggest a particular example for you based on your life experiences. Resilience, at its core, is the ability to overcome adversity or challenge in some manner. This could be from a personal or professional experience - think outside the box here! When was a time in your life when you really had to fight to get through a time or experience?
For what it's worth, if you feel comfortable using a personal example as opposed to a professional one, I would tend to use that: I think it shows more dimension to you as a candidate overall rather than everything being grounded in professional experiences. See, for example, my own response to this question in my last article:
In this week's (slightly delayed - sorry!) Article, we take a look at law firm interviews. Introduction Almost every law firm’s application process involves some form of interview. This style of interview is designed to find out about your motivations, experiences, skills and characteristics...
www.thecorporatelawacademy.com
(n.b.: it's phrased as "tell me about a time you overcame a challenge", but these are basically the same)