An agency, in the oldest commercial form of the word, is a company that takes action on behalf of another company. In the marketing world, it's a company that provides marketing, branding, and/or design products. It's to be distinguished from consulting companies that provide services.
An agency, then, is supposed to be an extension of a company. It starts with a company's goals and then acts as an extension of that company to provide products that support those goals.
The agency in this form has been around some 50 years or so. And the current question is "Does this approach make sense anymore?"