Interview for postdoc position in mathematics
Why should you be worried? This is a pretty standard postdoc position interview question and you should be prepared to answer it. 

I echo P.Windridge's comment:- your specific answer may be less important than a clear indication that you've considered how your research fits in, extends, challenges, tests the current state of the art in your field. 

You've set the problem of answering this question in the context of "real life", whatever that is. For your specific case, I would have thought the "real life" applications of PDEs is easily referenced.