"Design is the rendering of intent" — Jared Spool (link)
Design is about making deliberate changes to something (an object, a system, ...) in order to make it better.
The mission of the design leader is mainly to create the environment in which the design team performs to the expectations, i.e. serves customers with products they love, yet work for the business.
Design needs a fair amount of supporting activities to be done well
Inspire and motivate the team
Create, refine and share the product vision and principles, in collaboration with the product leader. In particular, help creating design artefacts that support communicating the vision.
Define and implement the design strategy
Improve design maturity in the organisation (help teams get a deeper understanding of the customer, understand and apply design practices (process, user research, ...))