See: http://www.whydomath.org/

Plenty of pure mathematics keeps turning into "applied" mathematics as time goes by.
That is the gist of how math impacts society. I would stay away from the more philosophical answers such as "Math helps you to think logically" etc., since your audience would probably not appreciate that. 
Some of the more apparent uses of high level mathematics:
1). Theoretical advances in control theory that lets us fly UAVs, supersonic planes etc: 
Lockheed Martin/Boeing/etc. often employ mathematicians (pure and applied) to work on control aspects

2). Theoretical advances in communication theory that has revolutionized the telecom business:
Companies such as Qualcomm,Samsung etc. employ many PhDs who work in theory.

3). Pure Mathematicians such Edward Belbruno (NASA/Princeton) helped devise new ways of interplanetary travel using exotic properties of the three-body problem.