You can kindof think of the fediverse stuff as being similar to email. You and I both signed up to create an account with kbin.social. This is where our account lives and it will show up in our full username (hover over any username) after the second @. You are @autumnplains@kbin.social and I am @sxt@kbin.social.
OP created their account with reddthat.com so that is where their account lives.
Unlike email however, we aren't sending messages directly to each other - we are instead sending them to a particular "community" which happens to live on the lemmy.ml server. This is possible since each of these hosts are running software which can communicate in a common manner (this is what ActivityPub defines the rules for). You probably got to this thread from kbin's general "threads" page which is able to list posts from other hosts due to them being federated (can communicate what posts they have to each other).
As for kbin.social being put next to the right of the title for this thread, I'm not sure. I think that might just be part of kbin's UI showing where we are viewing the thread from?
"Sync for reddit" was one of the more popular Android apps for reddit