What AMP stands for
The acronym stands for Accelerated Mobile Pages. The project started in October 2015, when news pages took several seconds to open on mobile and some platforms were offering closed formats as an alternative to the browser.
It is not a new language. An AMP page is still HTML, but HTML with strict rules. Custom JavaScript is forbidden, the CSS is inline and subject to a size limit, and images, videos or ads are declared through the framework's own components instead of the usual tags. A validator checks whether the document follows those rules, and only valid pages get its benefits.
Three things that tend to be lumped under the same word are worth separating. The first is the format itself, an open standard anyone can serve from their own server. The second is the Google cache, the infrastructure that copies and delivers valid AMP pages from a domain of its own. The third is the preferential treatment Search gave those pages, which for years was the real reason publishers adopted the format. The three have taken different paths, which is why the question about AMP no longer has a single answer.