Each server (or “instance”) of lemmy is completely independent, but instances can interface with each other through a standardized API to display content from another instance or interact with content from another instance.

When you use a client, it interfaces with your instance through its client API, which is also standardized.

I think Lemmy uses the ActivityPub protocol/API for client/instance and instance/instance communication, just like Mastodon, PixelFed and other federated social networks, so it creates a huge network of independent but compatible instances (and even allows compatibility between completely different social networks!) with no central authority or storage.

You can read more here about lemmy specifically: https://join-lemmy.org/docs/en/index.html

Here you can find more info about the Fediverse in general, which is what we call this federated network of instances of all the different softwares, including lemmy: https://joinfediverse.wiki/Main_Page