Wow'ing the customer is a more recent phrase in customer service and customer experience that means:
Vastly exceeding what customers expect and want from you in terms of how they are treated as customers.
Synonyms including "exceeding customer expectations, and "delighting the customer".
The Thought Behind Wow!
The thinking is that when you exceed customer expectations/wants and go way beyond what they want, the result will be a building of customer loyalty, and increased customer retention, in addition to fostering some powerful word of mouth recommendations.
That's the thinking, and it certainly holds true for some kinds of businesses, most notably high end hotels, restaurants and other businesses that charge high prices and have demanding customers. It probably holds true for other lower end establishments, but the problem is that businesses with lower margins may have difficulty WOW'ing and still making a profit.
Delighting Customers Not A Fix For All Business Issues
That said, the WOW!, the delighting customers doesn't fit for all businesses, and it's not completely free of negative side effects. See: Does Wow'ing The Customer Have Negative Side Effects?