Release Management for Visual Studio 2013 is a continuous delivery solution that automates the release process through all of your environments from TFS through to production, all in one solution, and all integrated with TFS.
Release management 2013 does not support integration with jenkins. Refer to this doc here. Also check out this doc for Release Management 2013 documentation in MSDN Library.
If you're just starting out with release management you should check-out the web based version. The server client version will not have any new features added to it.
Also check out this tutorial: Continuous deployment/delivery with Jenkins and VS Team Services