Traditionally, websites had an "admin" section built alongside the site itself. For example, to edit a Wordpress site's content the user would visit website.com/wp-admin.
A headless CMS actually runs on a different website, usually one provided by a third party e.g. pullnote.com or builder.io. Although at first this may seem more convoluted, it is actually considerably simpler to implement and maintain.
These benefits make infrastructure options much simpler - you no longer need a server with database / PHP etc capabilities so these sites can be hosted cheaply and quickly at the edge e.g. using Vercel, Netlify, Cloudflare Pages etc.