So I'm no expert. I've just been learning about this for the past 2 days and am not a STEM. I did some vocational training and OTJ experience when I worked as a computer net admin back from 2001-2004. That's all my computer admin experience.

Instances are like servers. Anyone with a Linux machine can set one up as the system is FOSS and the documentation and program is helpfully laid out here. Someone setups an instance and joins the federated network following the instructions. The instances then all communicate to each other and share what is going on in their instances. The person running the instance can make rules that block other instances based on each admin's preferences. That means that as long as the instance you are on is communicating with the other instances, then you guys can see each other's posts and comments. Not only that, but the federated network includes other interfaces that aren't just Lemmy because the instances communicate using the same language. That means that kbin, Mastodon, and Pixelfed can also interact with Lemmy. You can see their stuff too! Another analogy would by like email, except emails were all posted on reddit-, twitter-, and photo- like forums instead of between two parties.

So from my layperson's understanding, this is like if anyone can host a full "reddit" with it's own "subreddits". And if they don't like a particular reddit's layout, they can try another reddit that looks and interacts somewhat differently. Yet, all the separate reddits can communicate with each other, share info, and not one entity can control the system. Ultimately, if you don't like your instance, you can leave and create the exact same community in another one. That means there could be hundreds of the same "subreddits" throughout the federation. Or, if you want to run your very own Lemmy/kbin/Mastodon/Pixelfed, go for it. Be your own admin.

Personally, I think it's a pretty interesting and progressive approach to power distribution of the social media. As a political anarchist, I find it quite interesting and appealing.