Testing Hasura GraphQL APIs with Karate involves creating unit tests to ensure the reliability of GraphQL queries as changes are made to the API, highlighting the differences between testing GraphQL and REST endpoints. While REST endpoints typically return a 200 (ok) status for successful requests, GraphQL can return partial successes with errors, necessitating more nuanced testing approaches. Karate, an open-source test automation suite, is used to test Hasura's GraphQL API, offering features like browser automation, parallel testing, and Cucumber HTML test reporting. The process involves setting up a Docker environment, configuring tests with queries and variables, customizing headers, and employing assertion functions to validate responses and ensure data integrity. Tests are run within a Docker container, with results outputted both to stdout and a detailed HTML report, providing comprehensive insight into the API's performance and correctness.