You all know the Dropbox feature: "Sync this (remote) Dropbox with my Dropbox account". According to my (former) understanding of the term federation, this is the simplest use case of federation. Instead of "working remotely" on a "foreign" share, I sync the data to my account. Technically, it is not a copy, but more or less a symbolic link.
If you talk to federation experts or use the definition from Wikipedia, my understanding is not correct.
A federation is a group of computing or network providers agreeing upon standards of operation in a collective fashion.
In my example above, there is no group of computers. Dropbox is a simple SaaS offering. All under one domain with different customers. They can do what they want, or what their customers want them to do.
Your place or mine
Let me switch to a real world problem. With Cloudron (or other self-hosted technologies), YOU are the SaaS provider. Your teammates or family members can use tools like rocket.chat or Nextcloud. You are in the position of the administrator and add new users to your offerings. But what happens when your colleagues or family members follow your advice and step into the role of SaaS provider? They install Cloudron and then rocket.chat or Nextcloud as well.
Suddenly, you're in the situation where you're asked to participate in their app offering.
I personally have more than 5 different user accounts for different rocket.chats. The same goes for Nextclouds or Bookstacks, Vaultwardens and some other cool apps. Every time I change context, I have to change my user account too. That's fine for me, but is that the answer to every question? No, it’s 42!
This is where the Fediverse comes in
The Fediverse (a portmanteau of "federation" and "universe") is an ensemble of federated (i.e. interconnected) servers that are used for web publishing (i.e. social networking, microblogging, blogging, or websites) and file hosting, but which, while independently hosted, can communicate with each other. On different servers (instances), users can create so-called identities. These identities are able to communicate over the boundaries of the instances because the software running on the servers supports one or more communication protocols which follow an open standard.
In the Cloudron app-store we can find a lot of apps that are able to use federation protocols and functions. Therefore, I can have a rocket.chat instance and connect it to the instances of my associations and friendly companies. I have my own Matrix home server installed and easily connect my identity to other instances. I connect my Nextcloud to other Nextclouds and work on the same documents with the remote user base. Last week I wrote about PeerTube, this wonderful piece of software.
Sometimes you will see a red warning: Experimental function. Try it out. If you have problems, open an issue in the issue queue. We need more first movers for these kinds of features.