"Federation" is a word people use when they mean interoperability in the context of internet communication. It means that you can talk to people who aren't in the same network as you. If I use fastmail and you use gmail, I can still email you.
Most social networks aren't federated. If I'm mutuals with you on twitter that doesn't mean I can message you on facebook, and you don't see my instagram posts unless I explicitly cross-post them.
There's a pretty obvious incentive for companies that run these networks not to federate. Their primary asset is their users and the network effects that keep them from leaving. If the only social network you use is facebook and I want to read what you post online I need to make a facebook account and read your posts on facebook. Once I've done that facebook can show me ads, generating revenue for themselves, and show me other content to try to get me to spend more time on facebook. If I could follow your facebook account from twitter, facebook would have no way of making money off of me, and I would have little attachment to facebook.
Those same network effects also make it difficult for people to start new social networks. A user gets nothing out of a social network unless there are other people on that social network to talk to. If a new social network can't interoperate with existing social networks then it has to have a pool of users who want to talk to each other on day one. This is hard to do.
You can also try to piggy-back on top of one of the larger social networks by making it easy for your users to share content on those networks and having links back to you. But this is awkward because each of the larger networks knows that you're a potential threat to them, as they were to networks that came before them, and they also know that at the moment they're in a position of power over you. So as soon as it looks like you might be growing in a way that could cause a problem, they change the rules. The feed ranking algorithm changes. Your media embed or autoplay priveleges are revoked. The way your feed items are displayed is changed so they're not as prominent. The larger network usually justifies these changes as combating spam and obnoxious content, and they partly are, but there's also a clear competitive incentive behind them.
The result of this difficulty is that there aren't that many social networks. If you were on the internet in the early-to-mid 2000's you probably remember phpbb and vbulletin forums. These forums typically had tiny numbers of users, maybe in the thousands, and there were a lot of them. Because the software that powered the forums was easy to modify each one was hacked in some way that made it a little different from the default installation. Custom moderation tools would get built in response to things that happened on the forum; tools that only make sense in the context of the people who use that particular forum. In-jokes, memes, and local flavor would get added to the software. Features would get built that catered to things people did on that forum which were different from what people did on other forums.
Contrast this with networks like facebook, twitter, or snapchat. A centralized design team decides what is or isn't worthy to get built for everyone who uses the network. This means that they have to cater to the average of all their millions of users. Of course everyone is different from that average in some way, so really that means that it's an equally awkward fit for everyone.
If there's a critical mass of users that use social networks that other networks can interoperate with, then the micro-localization (localization down to the level of a social clique, not just a country) of the old forum model becomes viable again. The problem of getting a critical mass of users goes away because your users can talk to the critical mass that already exists in the rest of the federation.
Various attempts at this have been made, with varying levels of failure. identi.ca was the first one that I know of (unless you want to count old-school things like Usenet). identi.ca evolved into gnusocial, which evolved into qvitter and postactiv. mastodon is a new social network that's interoperable with gnusocial and friends with a slicker, more dynamic interface. Diaspora is probably the server that's gotten the most press, though it's only interoperable with other Diaspora installations.
I'm interested in this now because mastodon is the first of these that enough people in my social circle started using for me to get any use out of it. It's still tiny; as of this writing there are fewer than 400k mastodon accounts registered on all public servers combined, and I don't know what the number of MAUs is but it's going to be significantly less than even that.
By the numbers I shouldn't care about this thing. It is growing exponentially at the moment, but that's only been happening for the past month or so, and it could run out of gas at any point (that's just how these things are). But there's something about being able to fix the house you live in that makes you want to do it, even if you're never going to make that investment back.
And I think micro-localized, custom-tailored social networks are something worth having. It's fun for tech-savvy people in developed countries to be able to customize their social media, but it's absolutely essential for the countries that are just now joining the internet. As I said in this post, taking facebook and just translating the strings isn't going to cut it when you're in a country that doesn't just speak a different language but has different cultural assumptions and norms. Nigeria, Vietnam, Bangladesh need their own social networks the same as China, Russia, and Japan have their own social networks. If history repeats itself those networks will be isolated islands cut off from the rest of the world.
If Nigerians prefer Nigerian VK over Facebook (and Americans prefer American social networks over Nigerian VK), and Nigerian VK allows federation, then we'll be in a new equilibrium where it makes more sense to federate than it does not to, because there are big pockets of users that you can't capture even if you're the biggest player.
Do I think that will happen? Not really, no. It didn't in China, Russia, or Japan, and history repeats itself more often than not. But the fact that it could happen is making me exited about the internet again in a way that I haven't been in five years.