The Category Archive Page in Elegance will automatically display as you see here:
The posts associated with the particular category will display three across.
You will just simply need to add posts to a category then you can display a link to the category via the Appearance > menu option.
Another great way to feature a category is to create an image and add it to a widget area in a text widget linking to the category archive page using html like this:
<center> <a href=”http://YOUR UNIQUE URL/category/”><img class=”alignnone size-full wp-image-576″ src=”URL TO YOUR MEDIA LIBRARY IMAGE” ></a> </center>