What is the most important role in a scrum team?

Unquestionably this is the product owner.

Product owner is the the hub of the scrum team. They can make or break the team. The reason for this is that they hold the key to the story box. They are the visionaries ( sort of a product manager). At times they are also proxying for others. Many scrum projects fail solely because the product owner did not perform his role well.

The important functions among others of a product owner in no particular order are:

  1. Own the product backlog and in doing so the check book.
  2. Be the sole voice for requirements that the team can trust.
  3. Be the mediator to other interested parties in the organization and allow other stake holders to make thier case
  4. Communicate with the management on the status of the project.
  5. Be the main anchor in a sprint planning meeting.
  6. Prepare the backlog every sprint for the next sprint or so. Capture lots of detail for the upcoming stories while thinking a bit about the stories for future sprints.
  7. Be able to articulate what it would take for a developer so that he /she can accept the story as done.
  8. Do bug triaging.
  9. Train the users as the visionary of the product.