Customer Empathy is an ability to understand your customers on a deeper level. You would know who they are, what they are going through, their pains and problems. Providing empathy in customer service and other customer touch points, you allow the customer to feel heard and give them the power to interact with your company.
Being Empathetic does not mean you agree with all the points from your customer. It just means that you understand their perspective and can use it to provide the value to them using your product.