Jenkins is a continuous integration server. Integration tests take all the code and other components of your application and integrate it together, then test it to ensure it's working properly.
Jenkins can watch repos for version control software like Git or Subversion. When there's a new commit, Jenkins will check it out automatically. It will run your tests, and report the result. It can even be configured to automatically deploy your software to production if all the tests pass.
This course is going to show you all the basics of using Jenkins.