Accelerated Mobile Pages (AMP) for Google Mobile SEO, is an open standard for any publisher to have pages load more quickly on mobile devices. Back on Feb. 24, 2016, Google officially integrated AMP listings into its mobile search results. Basically, this means, that if your pages are AMP'ed, then your pages might appear higher in Organic Search Results and if your competition does not yet use AMP on their webpages for mobile, then AMP will give you that SEO edge you been hoping for. The Accelerated Mobile Pages (AMP) Project is an open source initiative that makes it easy for publishers to create mobile-friendly content once and have it load instantly everywhere. Enhance your AMP pages across Google. The Accelerated Mobile Pages (AMP) project is built on top of existing web technologies to enable blazing-fast page rendering and content delivery.
If you are wondering, how and where do I get AMP'ed... well, hopefully you have WordPress, and if so, you are in luck, because there is a FREE WordPress Plugin called AMP and best of all, its FREE.
I hope this helped clarify what an AMP site is.