Perelman's work isn't important because of its applications. It won't help anyone build a bridge, aim a rocket, crack a code, or privatize Social Security. Mathematicians, no dummies, like to point out that, in some unspecified future, Perelman's theorem might pitch in to help with these problems in ways that aren't obvious now. But its real significance is like that of the fact that a times b is equal to b times a; it's a basic structural statement about how the world is organized. If you prefer order to chaos, that's something worth caring about.
The obvious thing to say w/r/t this is the remarkable utility of Einstein's theory of gravity for geolocation (GPS) (Ashby has written much about this). Who would have expected in the early 1900's that a theory of gravity which provides very small corrections to the marvelously useful Newtonian theory of gravity would turn out to be essential for modern navigation and positioning?
But more than that, and it's hard to say this without sounding incredibly corny, this is a tremendous and unexpected achievement of our species as a whole. I'm not sure to what to compare it, but imagine someone comes along and runs a 2 minute mile. No practical benefit, but golly, what an achivement.