There is no magic, the servers just send it to each other.
So you send your post to LW, they store it and show it on their website. But they also send it to all the other Fediverse servers they are connected to (aka “federated with”), so those can also show it to their users. The same thing happens when a post is updated or deleted, or when new votes come in. The servers just send each other messages about what changed, so they can all act accordingly.