Imagine there were multiple reddit websites. Reddit.com, reddit.org, reddit.social, etc. Doesn't matter what account you have, you can see communities/subreddits across anyone of them.
That's Lemmy.
When you make a lemmy account, it's more like an email address. You are evolone@lemmy.ml, I am cosmicsploogedrizzle@lemmy.ml. Someone else is joeblow@beehaw.org. We can all chat and post and have a good time no matter what website/instance we post to.
That's how users work on lemmy. Just like email. Communities on lemmy work the exact same way as users.
If all you're interested in is that, then you can stop there and fully enjoy your time with lemmy as a reddit replacement.
The future potential and complexity comes from the next part:
The fediverse is someone said, "hey, you know how people on reddit can't follow people on Twitter, or people on YouTube can't subscribe to subreddits, or people on Instagram can't leave YouTube comments? Well let's make it so you can.
Now this isn't perfectly implemented at the moment, and there are a lot of growing pains (it's kinda like the wild wild West), but you can make a mastodon account (like Twitter), and follow the this lemmy community !asklemmy@lemmy.ml on it, and you'll see all the posts and all the comments that you would otherwise see on lemmy, just in a twitter-like format.
It's not perfect and compatibility across these decentealized apps is not perfectly impremented atm, but in the future you could theoretically have one giant interconnected web where everything from "Twitter" to "reddit" to "YouTube" to "Instagram" to whatever fediverse equivalent app are all interwoven. And if any instance of them gets a big enough head to pull something like reddit is pulling, or what Twitter has been pulling, the community can just make a new "email" on a different instance/website and continue as of nothing changed. No single website/instance can abuse their power, because another instance can be spun up any time.
Thanks! Feel free to cross post it!