To place 'Product Categories' within the 'Featured Categories' section, from the store dashboard go to:
> Products > Product Categories

From within this page click a 'Product Category' you'd like to place in the 'Featured Categories' or hover over a 'Product Category' with your cursor and click 'Edit':

From within this page scroll down to 'Featured' and tick its checkbox:

Just underneath 'Featured' you can select an image in 'Featured image':

Click 'Update' at the bottom of the page:

Once you've finished the above steps for all categories you'd like to feature, go to:
> Store Settings > Theme Options > Front Page

Scroll down to the 'Featured' heading and tick the checkbox 'Categories':

(*Don't forget to click 'Save Changes' after making alterations*)