A creative services firm is a company that provides creative services to other companies or to the public: they 'do creativity' to order.
Typical business models revolve around selling the time of skilled professionals, either on a project-by-project basis, or through a service level agreement and providing services on an ongoing basis for a fixed monthly fee. In this sense they share much in common with professional services firms but there are also key differences:
References
Creative services firm Wikipedia(Text) CC BY-SA