Keanan Koppenhaver explains over at WP Mayor: When and When Not to Use Headless WordPress:
If you have a strong frontend team that’s comfortable interfacing with APIs and is used to communicating changes and working with more distributed systems, then it might make sense for them to focus on the frontend of the site while a separate team works on the actual WordPress piece.
However, if you’re more of a solo freelancer or don’t have a lot of experience in more distributed systems, version control, deployment, etc, it might make sense to stick with a more traditional WordPress setup.
This is the best, briefest explanation I’ve seen of why Headless WordPress matters and who it matters to:
Headless WordPress can be a powerful paradigm that allows you to leverage modern technologies and bridge the gap between an editorial experience that content creators are familiar with, while still being able to use some newer tech that hasn’t come to the WordPress ecosystem yet.
A lot of writing about headless has focused on the technical “what” question. The when, why, and who questions matter much more.