Continuous Integration, huh ?
Simply put CI is running all the tests (against your code, system etc) frequently in order to perform code validation and see everything is integrating well with each other. For Example - If I check in Code then CI runs all the tests to see if the commit did break anything.
Why are we doing this CI stuff anyway ?
To check if something failed on regular basis, so that it is easy to fix it at the earlier stage.
Note - I am a mere mortal and follower of DevOps (much broader term) but have started to appreciate the simplicity all these concepts bring in. Don't mistake me for an expert here ;)
A little background on why I explored using Jenkins as the CI solution, the Project recently I started working on requires me to code in Python/ PowerShell and the team already uses Jenkins for other projects in Python, Java, Ruby etc so we needed to integrate running of Pester tests from Jenkins for our PowerShell codebase.