The MongoDB Atlas API allows developers to programmatically manage their database clusters, enabling them to launch, edit, and modify clusters with automation tools. The API provides a REST interface that includes features such as JSON entities, digest authentication, browsable interfaces, and security measures. Developers can use APIs from popular DevOps tools like Chef, Puppet, Ansible, and Terraform to automate common tasks, such as creating, modifying, and destroying clusters. By leveraging the Atlas API, developers can implement a fully codified version of their infrastructure, reduce deployment time, and scale or modify clusters based on needs.