A role is a combination of responsibilities which some person can assume. It requires a set of capabilities which the person needs to have. We think that roles are important in a Service Desk. Do not equate roles with processes, while a managers role will include responsibility over some process, there is more as a process is just one tool.
Processes work well in routine situations, where the results are predictable. It is good to have a set of efficient and effective processes running for common ITSM events. But processes will not make a great service or protect you from difficult situations. The real challenge lies in unexpected, complicated, complex or chaotic situations where there are no standard answers and any process is a waste of time.
A role is in charge of all kinds of events, the person acting the role needs to be prepared for unexpected events and reactions. Competense, experience and skills are important. The person needs to be capable of innovating new solutions to new problems when standard processes and procedures fail.
Roles should be defined, but not in a detailed and limiting way. A role is defined by the main value it creates and by the required capabilities. I hope this is obvious to most, but it is easy to misunderstand the ITIL process framework and see the roles limited to the processes.