Categories are a way of organizing your products so that customers can browse your site more easily, similar to manufacturers and departments. It is not absolutely necessary to use categories, but most sites are going to be improved by this kind of organization.
To create a new category, click Create Category. To create a sub-category of another category, click the + Add button in the parent category row. See this page for an explanation of all of the fields that can be set for each category.
To assign a product to a category, open that product under Products > Manage Products, open the product in the grid view and click on the Mappings tab. Check the boxes next to the Categories you'd like the product to appear in and click Save.
Displaying Sub-Category Images
By default, sub-categories will display in a list near the top of the parent category page as shown below:
Optionally, sub-categories can be displayed in a grid with images by changing the SettingShowSubCatsInGrid to Yes.
Once this is set, the sub-category list will be replaced with a grid with sub-category images as shown below: