AMP stands for accelerated mobile pages and is a way to have page content render quickly. AMP URLs can be seen in Google's mobile search results as identified in SERP Features. Oftentimes they appear in the Top Stories or News section but will also appear in the standard web results as well. This will be indicated via a designation that says AMP.
AMP's are restricted in what they can display so that the page can be loaded quickly (less than a second) and reliably. Without getting too technical there are 3 primary components to it: HTML (hypertext markup language), JS (Javascript), and Google's cache. Google will cache AMP pages and serve them up through their own CDN (content delivery network) but with their own designation.