In the majority of the traditional style projects the customer is involved, but in a limited capacity. They get to participate in scope definition during initiation and planning, but then any changes they deem necessary are change ordered back to them. This practice assumes that the customer knows exactly what they want up front and penalizes them for changing their minds later in the development process.
Within Agile the customer maintains control; they are even responsible for achieving the projects return on investment (ROI), by choosing features with the highest business value. They own the scope, priority of what gets implemented and when, and define the release plans for the product. In short, the customer is an active participant, not a spectator as in a traditional waterfall style project. When the customer is engaged throughout the development lifecycle they are more bought in and committed to the project, therefore improving the overall chances for a project success.