This is an archaic Italian word for being able to do your craft without a lot of visible effort. It's a combination of elan and grace and class, sort of the opposite of loud grunts while you play tennis or a lot of whining and fuss when you help out a customer.
Many people are unable to put their finger on it, but this is a magnetic trait for many of us. We want our lawyer, dentist and waiter to demonstrate sprezzatura, but of course, not particularly try to. This is one of the secrets of Danny Meyer's top-rated restaurants in New York. It doesn't have to be flashy, it doesn't even have to be the very best there ever was, but sprezzatura is enough to get us to return. As long as this light-footedness is scarce, it will remain valuable.