It uses activity pub, a protocol that allows servers to share content. So when you post on an instance, it became available for other instances to consume your content.

About slowness, it can be that your instance it being rate limited, or it is not powerful enough to process all its users. You can try another instance.

Activity pub documentation: https://www.w3.org/TR/activitypub/

If you’re replying to a community on your home server, all actions should be similar levels of responsiveness, I think replying to another servers community may involve “some” active communication with the instance? Simple way to test this, if you are replying a lot on to another servers community, since you are browsing anyway, would be to just open the server/community directly and click around, if it’s feels a bit slow, then that server is overloaded by a bit and that’s probably the source of your issue. Otherwise we need someone with deeper knowledge in this thread.

I’ve never admined a lemmy server but rate limits are probably why it feels slow.

Federation works by each server sharing new activity with each other and rate limits help not crash the server or accidentally DOS smaller servers.

Your server sends a message to other servers saying what you voted or replied.

A reply dialog being slow to open sounds like an issue with your client, not federation.

I have no idea how any of this works. Im just happy to be here.