Alom Shaha, a science teacher at Camden School for Girls in North London, produced an excellent film that asks, and answers, the question ‘Why does science matter?‘ (via Guardian Science Blog).
If nothing else, it might help young scientists articulate an answer when faced with the question; it isn’t enough to have that warm, secure feeling of knowing that science is important in yourself, you need to be able to communicate this without getting bogged down in detail.
Also take a look at Alom’s other science short films.