In one sentence
llms.txt is a plain-text file placed at the root of a website that gives large language models a curated, markdown-formatted summary of the site and its most important pages. It is a proposed convention, not a standard, and it complements rather than replaces robots.txt and sitemap.xml.
A good llms.txt opens with the site name, one blockquote-style sentence describing what the organisation does, then grouped links with a short description each. A companion llms-full.txt carries the full text of those pages for models that want the content without parsing HTML.
Support is not universal and it should not be your main lever. Treat it as cheap insurance: it costs an afternoon, it removes ambiguity about what your site is, and it is trivial to regenerate at build time so it never goes stale.