TL;DR both of them speak the same language so both can call each other up and trade info back and forth. You can upvote/comment/whatever on either and it’ll appear on both sides without you having to do anything special.

It doesn’t all go back to lemmy, but lemmy and kbin speak the same language (ActivityPub) and can talk to each other (they are federated). Others in this thread have compared it to email where you might be on different services (gmail, yahoo, icloud) but they can still all understand messages coming from each other. The fediverse is similar, but instead of just sending a message to another site to put in your inbox like email, lemmy/kbin/mastodon/etc can ask each other for stuff on an external site and display it to you as if it was all coming from the same site.
In our case kbin calls up lemmy.world and asks for what everybody there is saying on some post. Lemmy.world tells kbin about all the comments and upvotes so kbin can plug it into the same style of page you see for everything else here. Even though it’s happening on a separate server and underlying platform, they still know how to exchange data