This is a widgeted area which is called Home Bottom #4. It is using the Genesis - Featured Post widget to display what you see on the Executive child theme demo site. To get started, log into your WordPress dashboard, and then go to the Appearance > Widgets screen. There you can drag the Genesis - Featured Post widget into the Home Bottom #4 widget area on the right hand side. To get the image to display, simply upload an image through the media uploader on the edit post screen and publish your post. The Featured Post widget will know to display the post image as long as you select that option in the widget interface.
