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.