Basically sprezzatura describes a level of service that looks effortless. It's the opposite of whining when customers ask for something beyond the norm. It's a feeling of strong eagerness and grace that makes the person providing the service look like it's easy and a pleasure to deliver. The great thing about this is you won't necessarily find this trait at the number one retailer, the best restaurant, the top rated ad agency - often it's the smaller, less well known businesses that know how important it is to "wow" the customer.
In the web world sprezzatura is the internet service provider who goes the extra mile to make sure broadband high speed really means broadband high speed. Personally it took at least 5 calls to my service provider to find sprezzatura in a single repairman who really listened and did more than just "check the lines" without being asked.
It's the web development pro who understands in advance that does more than what was requested because it's the right thing to do for the website and customer.
For example: Noticing that the navigation with keywords is in images (without alternative tags), knowing that text is read easier by search engines, and taking the extra step to add the alt tags and text navigation at the bottom of the page - without being asked. The customer may not notice but when the search engines give the sites a lift, it looks effortless.
Another example: Adding a call to action message and easier access to the order / contact form by removing unnecessary steps. The customer only notices that suddenly they are getting more contact requests (conversions) from the site. Again, it's very much appreciated and looks like it was no trouble at all.
My premise is this: Everyone expects sprezzatura, very few deliver. As long as it's a rare trait to find, the value for this service will remain high and will be well rewarded.