There are 3 elements of a parent-child relationship:
The parent product is a non-buyable product used to relate child products. The Amazon catalog uses the parent product to establish relationships between the child products. For example, if 2 shirts have the same parent then they are related and are considered child products.
The child product is an instance of the parent product. You can have many child products that are all related to one parent product. Each child varies in some way, for example, by size or by color.
The variation theme defines how related products differ from each other. For example, in the Clothing, Accessories & Luggage category, child products can differ from each other by size or color.
You can also use hybrid variation themes. For example, the Clothing, Accessories & Luggage category supports variations by both size and color, so you can use "SizeColor" as a variation theme. See the valid values tab in the inventory file for your specific category to see which types of relationships it supports.
The images below shows a product with size and color variations. The parent product is a t-shirt with no size or color product details. When a customer views the detail page, they see the child attributes of color and size.