The category index page is a special page to showcase your post categories.  This page uses the Category Index Widget in the Appearance > Widgets area.

You will first need to add a new page.

Name it Category Index or whatever you would like.

Select the Category Index Page template.

Leave this page blank and publish.

Now you will navigate to Appearance > Widgets.

In our demo site we have the following widgets in the Category Index Widget area:

to feature each of your categories, you will drag a new Genesis – Featured Posts widget into the Category Index widget area and select a new category.  Each featured post widget should be configured like this: