Jenkins is an open source automation server written in Java that provides continuous integration (CI) services for software development. It can be started via command line or as a web application, running on a servlet container like Apache Tomcat. Jenkins has over 1000 plugins, making it easy to create and automate builds. Continuous integration with Jenkins involves frequent code commits triggering automated builds, compilation, unit testing, and source control integration to provide feedback. The document advertises an online course teaching how to use Jenkins for continuous integration, available for $15 using the coupon code "OFFER15".