Product categories often overlap. Sometimes, a product could belong to more than one category. Let’s take the example of a clothing store. You could have a men’s category and a women’s category.
This creates a little problem for unisex items like socks and t-shirts. Where do you keep them? You could solve that problem by either having separate categories for unisex items or duplicating them as sub-categories under each of the parent categories.
That brings us to problem number two. Let’s say you have a men’s parent category. You can have sub-categories like shirts, pants, and casual wear. Take an item like sweatpants. They could logically belong to either the pants or casual wear sub-category. A lot of sites may classify sweatpants under casual wear but quite a few customers feel that sweatpants have as much claim to pantshood as jeans and corduroys.
It is this fuzziness in category borders that makes it necessary to have sub-category links. They clarify what’s included within the parent categories and massively simplifies navigation for visitors on your site.
In the homepage categories section
These links help users decide which path they should take to find the product they want.
It also helps returning users bypass intermediate pages and go directly to the sub-sub-category they want.
Not common
I looked at 55 of the top ecommerce stores, and haven’t found a single one that is doing this. However, most of them have at least a thumbnail to illustrate the category, and several of them also added a label.
An alternative
Instead of putting 2 or 3 levels of navigation links in the categories section of the homepage, you can instead have a section with the main categories, followed by a section which allows users to browse through sub-categories.
Sub-sub category links
If you have a section to browse sub-categories, you could possibly put sub-sub category links under the sub-categories.