Pets Theme by default showing categories with featured products. If no products would be associated to categories, then it would be not displayed, like below:
To add products to those categories, just go to your administration panel to [Catalog/Categories] and choose those category which one is displayed on home page (in my case it would be Electronics and Apparel).
To add product just hit Add a new product button.
Please do not forget to check “Is featured product?” setting, other way it would not be visible as carousel.
If turn on all settings (including Widgets.Ajax plugin installation), and add also products for second category, final result would be as below: