A Center of Excellence (CoE), sometimes called a Center for Excellence (C4E), is a group of people with specialized skills and expertise whose job is to provide leadership and purposely disseminate that knowledge within your organization :
https://www.pmi.org/disciplined-agile/people/centers-of-excellence

An Agile Center of Excellence (ACoE) is a team or group within an organization that is dedicated to promoting and supporting agile practices. They are typically responsible for educating and training employees on agile methodologies, facilitating the adoption of agile practices, and ensuring that agile principles are being applied consistently throughout the organization.

“A CoE serves as the primary resource or Single Source of Truth for Agile practitioners within an organisation,” explains Patrick Fitzgerald, a senior consultant in Los Angeles

A Value Delivery Office (VDO) is similar to an ACoE, but with a more focused objective. A VDO is typically tasked with optimizing the delivery of value to customers through agile practices. They are responsible for measuring and monitoring the impact of agile practices on customer satisfaction, and for identifying areas where improvements can be made to further enhance the delivery of value.

Missions of ACoEs

The mission of an Agile Center of Excellence (ACoE) is to promote and support the successful adoption and implementation of agile methodologies within an organization. Some of the key missions of an ACoE include:

1. Education and Training: Teaching agile methods, concepts, and best practices to all personnel.
2. Best Practices Development: Creating and promoting agile project management and software development best practices, including Scrum, Kanban, and Lean.
3. Process Improvement: Finding ways to simplify, eliminate inefficiencies, and boost efficiency and effectiveness.
4. Agile Coaching and Mentoring: Helping teams and people across the company implement agile methods.
5. Collaboration and Communication: Promoting openness and understanding via team and department collaboration and communication.
6. Metrics & Measurement: Establishing and tracking metrics to evaluate agile methods and find opportunities for improvement.

By fulfilling these missions, an ACoE can help organizations to effectively adopt agile methodologies and principles, and to achieve greater success in their software development and project management initiatives.

Both ACoEs and VDOs are designed to help organizations implement agile methodologies more effectively and to drive better business outcomes through the use of agile practices. They are typically staffed by experienced agile practitioners who can provide guidance and support to teams throughout the organization, and who can help to ensure that agile principles are being followed consistently across the organization.