When I tell people that I'm studying mathematics, I usually get that typical look lying somewhere between surprise, admiration and math-was-my-worst-subject-at-school. The second question is usually what I want to do after my study — teaching perhaps?
Mathematics has been defined as the science of patterns and numbers. It is the basis for many things in science and technology. Most of mathematics at school is doing calculations, and many people don't see the use of all that or are having difficulties with it. Of course everyone has different interests and talents, but if you get past those basic high school things, you'll be able to discover the wonderful world of mathematics!
Math can be used to model all kinds of real life phenomenae. Using these models we can predict their behaviour, and this can be used to make (important) decisions or save a lot of resources and money. Mathematics has important applications in physics, but also in computer science, transport and logistics, industry and banking. But most of all mathematicians like to solve mathematical problems and puzzles.
Mathematics can also be used to create nice graphics like fractals or geometric shapes. For a small example, see my page on solids.
And who said mathematics is nothing for girls? The (Dutch) weblog www.wiskundemeisjes.nl is maintained by two female PhD students from Leiden University.