Without multiple instances, Lemmy would effectively be more like reddit (one entity controlling the whole thing). If that instance goes down, or it decides you can't talk about topic X, or it does anything that affects you as a user -- you have no option but to love it or leave it.

With multiple instances, if one becomes trouble, you just move to another. You can read and post to other instances from any other federated instance, so you get some freedom in that regard, and you're not really tied to any one entity (you're always beholden to the rules of your home instance, but you can also freely instance hop).

The best reddit analogy is probably using subreddits: imagine if one subreddit actually ran the whole site. R/spez one day decided to change the rules on yoiu, and you disagreed-- what option do you have? Well, in that setup, you simply start interacting on other subreddits. Lemmy kind of works this way, but there the subreddits are instances which control your login info, and there are communities within those instances that everyone elsewhere on the site can access.

The related technical advantage is still that no one instance runs the whole federation. Lemmy.world is big (likely because a lot od ex-redditors thought it was the one to switch to), but it doesn't control the rest of the federation. If it got shut down, for example, users on it would need a new instance, but the federation itself would be exactly as it was.

It's kind of like grass-roots networking, if that makes sense to you. One could also argue it's a bit like like bittorrent for forums.