The Style Dialog can be opened by clicking on the "Style Dialog" entry under the "Object" menu. The dialog is divided into two panes. The top pane contains a list of CSS selectors that are defined in the SVG’s first style element. The bottom pane contains a list of CSS properties with their values as defined by the selector chosen in the CSS Selectors Pane, and if an object is selected under the chosen selector, as defined by the style attribute of that object.
Selecting a selector in the CSS Selectors Pane will select on the desktop all objects that match that selector. Selecting an object on the desktop will select the first selector in the CSS Selectors Pane that matches that object. More details can be found at http://wiki.inkscape.org/wiki/index.php/Style_Editor.