Besides what Sonia suggested, also take a look at the classic What is Mathematics by Courant and Robbins. It is a bit long, so I am not sure how much you can pick out of it in one week, but good luck. For preparing your talk, you may want to consult some of the advice given by VI Arnold.

A good way to start any general discussion about mathematics, I think, is to remind people of the definition of the word mathematics. The original Greek term, μάθημα, means study/learning/science, which I think says a lot about the typical, somewhat idealized, mathematical worldview. That said, your work is significantly harder than that would be mine were I in your position. Large cardinals, set theory, and logic are much harder to explain to the average audience than something pedestrian like PDEs or sexy like mathematical physics.