The Workflow API lets you run workflows - specifically API workflows - on a POST request. By using such API workflows, you can create things, sign users up, send emails, and leverage plugins to access external services. Define the workflows as you would for a normal page, action by action. But, API workflows are one type of backend workflow, meaning they run independently of any page of your app and thus some actions (e.g. element-driven ones) are not available. Such an API workflow can return data, but for Read API calls, please use the Data API.
You can create API workflows after checking the box 'Enable Workflow API and backend workflows' in the API section in the Settings Tab. These workflows are defined in the Backend workflows page found in the Application Menu above the Palette.