A headless CMS is a content management system that separates the backend (where content is created and stored) from the frontend (where content is displayed). Popular examples: Contentful, Strapi, Sanity, and WordPress itself used headless via API.
The SEO advantage is that you can use any frontend technology (Next.js, Nuxt, Astro) to build an extremely fast website, while the content team works in a friendly backend interface. That results in excellent Core Web Vitals and total design flexibility.
The downside is complexity: it requires a technical team to implement and maintain, and features that are trivial in WordPress (installing an SEO plugin) have to be built by hand. For companies with a technical team and advanced needs, it is worth it. For smaller companies that need autonomy fast, traditional WordPress remains the more practical choice.