From the OP: "I hope to explain what math research is like, why it is important to society and how it differs from research in other scientific fields."

Three goals in one hour are a lot. The first alone is already difficult, but one attempt in this direction is a movie, "Colors of Math". It conveys, to adults, a hint of what it feels like to do math. You could do worse than show it to your audience. Yuri Tschinkel, at NYU, is connected with it and would, I imagine, help you to get a copy.