Select the promotion level for a build on the build status page. "Update Run" permission on the project is required to promote a build. The promotion level is shown on the build status page and the icon image is shown in the Build History on the project status page.

The promotion level and a numeric index value from the list above are made available in the remote API, so queries may be done for particular promotion levels. Example:
http://my-jenkins/job/MyJob/api/xml?xpath=*/build[action/levelValue>=2][1]&depth=1
This query finds the latest build promoted to the second or higher level.

All builds run after this plugin is installed will be promotable. To enable the promotion control for an older build first use this magic URL:
http://my-jenkins/job/MyJob/{build#}/parent/parent/plugin/promoted-builds-simple/makePromotable