Why a website can work with no connection
The mechanism is a service worker: a small script a site can register, which the browser keeps and runs on that site's behalf — even when no tab is open. It sits between the page and the network. When you ask for a page, the service worker can answer from a copy stored on your device instead of going out to the internet.
That's the whole trick. There's no app store, no download, no install size to speak of. But it only works if the site's authors chose to add it, and it can only serve pages you have already visited at least once. A service worker can't guess what you might want later.
This is also why "installing" a site is less dramatic than it sounds. You're not downloading a program — you're telling the browser to give an existing site its own window, its own icon, and permission to keep its cache around.