Writing the overview section
About the Overview section
The overview explains what you can do with the API (high-level business goals), and who the API is for. Too often with API documentation (perhaps because the content is often written by developers), the documentation gets quickly mired in technical details without ever explaining clearly what the API is used for. Don't lose sight of the overall purpose and business goals of your API by getting lost in the endpoints.
Sample overview
The SendGrid API does a good job at providing an overview:
Common business scenarios
In the overview, list some common business scenarios in which the API might be useful. This will give people the context they need to evaluate whether the API is relevant to their needs.
Keep in mind that there are thousands of APIs. If people are browsing your API, their first and most pressing question is, what information does it return? Is this information relevant and useful to me?
Where to put the overview
Your overview should probably go on the homepage of the API, or be a link from the homepage. This is really where you define your audience as well, since the degree to which you explain what the API does depends on how you perceive the audience.