This means that the website would be the tool to send and receive interactions; it would be the storage for all one's content.
This is to avoid those situations when content is removed, censored, etc. on a silo/social network; to have control over your own data and to have a mesh-network-like layout of individual sites that are more not single point of failures in opposition of gigantic monoculture that currently rule the internet.
The reference for the 'like it was all along' is a reminder that a very long time ago the internet was a network of individual websites and you were not bound to use centralized services from corporations.
My personal opinion behind the indieweb is here, in case it makes more sense like this: https://petermolnar.eu/journal/indieweb-decentralize-web-cen...
I think the coolest bit is that each of the pieces is so simple that a coder can get up and running from scratch in an afternoon. That's very different to a lot of the federated social web technologies to date.
What's the selling point there?
I like the idea of the IndieWeb, but can you tell people how to get started without such nitty-gritty details?