Normal assets like those you list are cached on download. "Local storage" is a bit more like cookies in that the webmaster can store whatever they like there. https://developer.mozilla.org/en-US/docs/Web/API/Web_Storage...

He's referring to the one of several APIs like https://developer.mozilla.org/en-US/docs/Web/API/Web_Storage... or those listed on https://www.html5rocks.com/en/features/storage - Allowing the webpage to store some amount of data on your local machine. This storage can be accessed even if you're temporarily offline, so you can have an interactive webpage that downloads some data, and so long as you don't close the page you can update it. When you reconnect (or next load the webpage) your state is stored and can be reconciled with server state.

For obvious reasons, you don't want that API active for private browsing (As persisting it would enable tracking), but by combining browser version detection to determine if a browser supports the API with feature detection to see that it's disabled, you can assume that "Private Browsing" is on.

Better browser API design might include in-memory only support for the API, but I haven't thought that all the way through.