Headless eclipse (or headless RCP) is the eclipse based application that doesn't have the GUI.
By making eclipse application headless, one can execute eclipse application inside eclipse without invoking heavy GUIs to speed up the whole development process.

This is the page that teaches how to make headless eclipse
Headless RCP - simple
Headless RCP - standalone
Headless RCP - with many plugins

Old pages for reference.
headless