Lemmy is like a city where people come to hang out, talk about their interests, and share news or ideas. Just like a city has different areas (like a park, library, or a cinema), Lemmy has 'communities' which focus on different topics like science, books, movies, technology, etc. You can post, comment, and vote on the stuff you like in each community.
Now let's talk about the Fediverse. Imagine if each city (like Lemmy) could talk to one another and share things. So, if your friend lives in another city (or uses another application like Mastodon), you could still talk to them, share news or ideas, and continue to hang out together. This whole network of cities communicating with each other is the Fediverse. It's a big neighborhood where different online platforms talk to each other, even though they're not the same or owned by the same group.
Just like in your city, you have a house (your account), on Lemmy, you live in lemmings.world. The '@lemmings.world' after my name is kind of like telling people my address, so they know where to find me.