Headless Odoo is an architecture in which Odoo is used as the backend (the system of record for products, customers, orders, inventory, accounting and business logic) while the user-facing frontend is a separate application (a Next.js website, a React Native or Flutter mobile app, a custom portal) that communicates with Odoo through APIs instead of using Odoo's built-in web interface.
The point is separation: Odoo does what it's excellent at, and the frontend is built with the tools that give the best customer, member or supplier experience. Multiple frontends (web, iOS, Android, a supplier tool) share one backend and one API.
It's also a commitment. Two codebases, an API contract to maintain, and a frontend that has to be hosted and evolved. Headless is the right architecture for some businesses and the wrong one for others, and this page is meant to help you tell which.