The customer role is similar in the agile development practices of Extreme Programming and Scrum. Although in Scrum the customer practices are more thoroughly defined. On the other hand, in Extreme Programming the engineering practices are better defined.

The customer has the responsibility to steer the project to successful completion and is responsible for these kinds of things:

• Create a product Vision
• Maintain a product backlog of features
• Split features in to small pieces of work
• Choose the feature content of each iteration
• Define acceptance tests for each iteration's deliverables
• Negotiate delivery dates and content
• Work as a team with development

That is a lot of work! Keep in mind it is not just one person. The customer roles is led by the product owner, usually from product management. The product owner leads a skilled team that knows the product domain and has a vision of the product they expect to be successful in the market. This team is usually made up of marketing, systems engineering and test automation.  One of the customer practices key to the success of the product is creating a rich suite of automated tests.  Who would be better at knowing what to test than those expert in the market's needs.