Summary - Not all features are important for every site, but most sites will benefit in some way by utilizing the features made available by Progressive Web Apps.
You can cache certain parts of the site on the user's computer, much like a native app. So when the site is visited the cached parts will appear almost instantly while any new or updated data will be the parts of the site that need a network connection. By cutting down on the majority of network connectivity the site will load dramatically faster.
Using push notifications is a great way to get a user back to the site. Let's take Brain Bank, for instance. If a user gets a new follower, or a post gets new love, we can send a notification to the user to let them know about the new activity. This will bring the user back to the site and keep them engaged with the content.
Click the article source to see all of the stats from sites like Uber and Wal-Mart on how they dramatically improved customer retention as a result of instituting new PWA's.