What is a PWA? I am being serious! I really do not know what it is? And I think most people do not know either!
PWA (which stands for "Progressive Web App") is a website that can be saved or installed and behave as if it were a standalone application. This includes things like launching full-screen with no web browser UI elements, appearing with a custom icon on the home screen, and support for things like push notifications, badging, geolocation, media streaming, and video/microphone access. Google's requirements for a PWA to be installable is that it includes code to properly handle offline modes, so that the web app can launch successfully (but maybe not "work") even when not connected to the internet.
Apple has never used the term "PWA", preferring instead of refer to the various web technologies individually. Some of those technologies have been supported in Safari since the very early days of iOS (such as geolocation support), and some of those have only recently been introduced (such as push notifications and badging).
The idea of "progressive" in PWA is that it can work normally as a website in a browser, but you can get some deeper system integration by installing or saving it. On desktop, this means that it launches is its own window and shows up as its own icon in the Dock. On iOS, this built on the (long-existing) add to home screen functionality, but recently started only exposing some functionality to web apps that had been saved.
I use PWAs for some social media sites, where I don't want to install an app that has full access to my device for tracking and advertising purposes, but I want something that can notify me when people mention me in a post.