The term “headless” comes from the concept of chopping the “head” (the front end, i.e. the website) off the “body” (the back end, i.e. the content repository).

https://en.wikipedia.org/wiki/Headless_content_management_system

Meaning that you would use WordPress to manage your content including your WooCommerce store settings and products in the back end and access the content via the REST API for the front end.

Capabilities of three REST API’s

The WordPress REST API allows you to manage your site and content in the back end while still providing front end options such as viewing a post/page, archive’s or even search.

WooCommerce REST API only allows the shop manager/s to manage the store settings, products, customers, orders, sale reports etc. All that handles the back end of things which requires authentication of the shop manager in order to create, edit or delete.

An example of WooCommerce running headless is their mobile app on iOS and Android which allows you to view orders, sales report, reviews and in progress as of writing this, products.

CoCart REST API allows you to control the products that are added to the cart via the front end as well as applying a coupon, selecting a shipping method etc. No authentication is required, unless a customer is returning and wishes to login.

All three API’s together will allow you to create a headless store in any language on any platform of your choosing and all are well documented.