Pure Math is Math done for its inherent beauty, or because of the interest of the Mathematician. It is the art of rigour, with naught but dreams holding it aloft.
This does not mean it has no application. Despite mathematicians' efforts to the contrary, people keep on coming up with ways to use the stuff.
RSA is a famous application of Pure Math, while Andrew Wiles' proof of Fermat's Last Theorem is an applicationless instance.