Have you done any research into how likely it is that a visitor from your demographic understands what "federated" means in this context? I ask because it's part of the tagline, so if you don't understand a key word in the product description you're probably less likely to show interest in it.
In this context, it means that content from this service is shared with other servers. This is different from decentralized - in a decentralized network, every client communicates directly with other clients, whereas in a federated network, clients communicate with central servers but the servers can interoperate . Email is a good example of a federated network - mail clients communicate with centralized mail servers, but mail servers can send messages to other mail servers. To extend that analogy, when you write an article on Write.as your browser sends that data to the Write.as server, but the server federates that data to various other servers - Mastodon instances, Pleroma instances, etc. This is what enables Mastodon et. al users to like, follow, and share content posted to Write.as.
Glad someone pointed this out. I had to Google it, then urban dictionary, then back to Google with an “open source” appended to the query, only after happening upon these comments. So far, I think it means “decentralized”
It does not mean exactly the same thing as decentralized. It is true that it is not fully centralized with one party controlling everything, but it is also not fully decentralized with each user running their own server.
Instead, multiple servers run by different parties share data with each other. End users can use the system without running their own server.