Workflows are one of the most essential pieces to the HubSpot marketing software, because it, along with Contacts and email, is at the heart of marketing automation. Using workflows, users can set up sophisticated marketing automation campaigns that rely on triggering relevant and timely actions (like emails) for contacts in their database.
For an example of how a user would set up a workflows inside of HubSpot, you can sign up for a developer portal for access to a sandboxed instance of the workflows tool. The Workflows user guide is also a great resource for understanding how a HubSpot user thinks about setting up and deploying workflows.
The Workflows API allows for full CRUD acess to any workflow in a given portal. The most often use case for the API is to first create a workflow for marketing automation, and then enroll a contact in that workflow based on some trigger in an outside application.
Workflows also has a powerful webhook feature that allows an outside application to receive a notification when a contact meets a certain set of criteria. If polling the API becomes too much of a hassle as you develop an integration with HubSpot, this is a great alternative.
For any specific questions about the Contacts API, refer to our developer forum, where many of the common questions have already been asked.