Federation means that instead of one central server like Facebook or google, the service relies on several interoperable servers and you can pick which one you want to sign up with and use.
Email and lemmy are federated. If you want to use email, you can sign up for an account on one of many different servers run by other people or you can even host your own email server. No matter which you choose, you can always email another user regardless of where their account it.
zalgotext@sh.itjust.works 5 weeks ago
So, non-federated means one company/organization has full control over some product/service/website (like Twitter, Reddit, etc).
Federated means that individuals can independently run instances of some product/service/website, and all those instances can talk to one another and share/sync data (Mastodon, Lemmy, etc).