In a standard Shopware install, the storefront, what a shopper sees and clicks through, and the backend, products, orders, customer records, are part of the same system. Going headless means pulling the storefront out of that picture and replacing it with something custom, a Vue, React, or other frontend, that talks to Shopware only through its Store API rather than rendering Shopware's own templates.
The appeal is real: a team gets full control over the shopping experience, can build it in whatever stack their developers already know, and isn't boxed in by Shopware's own theming system. Shopware built the Store API specifically to support this, so it's not a hack layered on top of a platform that wasn't meant for it.
What doesn't come free with that trade is anything the old storefront used to handle automatically. Search, filtering, cart logic, checkout flow, all of that lived inside Shopware's storefront templates before, and now it has to be rebuilt in the new frontend, calling the Store API for every piece of data it needs.