"EditStyleDefintions" is a front end token that lets you edit the style definitions for the current notebook.
This token is equivalent to the menu command Format Edit Style Sheet.
If the current notebook is using private style definitions, the style notebook is opened.
If the current notebook is using a shared style sheet, a dialog box will appear asking if you want to import a private copy of the style sheet or edit the shared style sheet.
To execute a front end token, you typically evaluate a command of the form FrontEndExecute[FrontEndToken[token]].