Component testing, an essential process in software development, involves independently verifying the functionality and performance of specific parts of an application, distinct from the entire system. The tutorial highlights the use of Cypress for component testing, contrasting it with end-to-end (E2E) testing, which validates the entire application flow. Component tests are quick, reliable, and require minimal setup, focusing on individual features like input fields in React components. By employing Cypress, developers can mount and test components independently, simplifying the testing process and reducing development time. The guide further explains how to configure Cypress for a React project, detailing the steps to write and execute component tests, and concludes with instructions on automating these tests using CircleCI, ensuring continuous integration and deployment.