Bluemix is IBM's cloud platform that allows users to build, run, and manage applications. It provides flexible compute options including Cloud Foundry, Docker, and OpenStack. Developers can choose from a catalog of services to extend their applications and deploy apps on Bluemix Public, Dedicated, or Local. Bluemix offers dev tools, integration capabilities, and pricing models including free trials and pay-as-you-go to help developers rapidly develop and deploy applications.