A headless CMS is Content Management System (CMS) where the data and authoring process is independent of the rendering.
A content author controls the data (which is structured, see below), and a developer can access the data via an API, and then can render as they wish. 'Render' here encapsulates both the resulting UI, but also the underlying architecture, infrastructure, servers, etc.
Headless CMSs often push the idea of 'structured content'. The content itself is broken down into smaller building blocks that can be shaped and rendered as needed. You don't have to succumb to page templates and a page consisting of just a Heading + Body. Each section can be a content block. e.g. FAQs become a 'Question' and 'Answer', rather than two lines of text lumped in the rest of the body. This FAQ data can then be represented on different pages, in different places, and in different ways.