The AMP cache checker checks whether a website is already indexed in Google-AMP-Cache and can therefore be output more quickly via Google search.
Part of the load time optimization for Google AMP pages consists of saving it in the search engine cache of Google search. AMP pages are loaded directly from the faster Google server instead of the actual server of the website.
You can use the AMP cache checker to check whether one of your URLs has already been included in the Google AMP cache or not.