It works a lot like like email between instances. Let’s call your self hosted instance “A” and the popular remote instance “B.”
User on A searches for “poodles” and finds a community !poodles. When they click the search results: A sends B mail saying “send me the last 10 posts for poodles.” B sends A mail with the posts and the user sees the posts, but none have comments.
If nothing else happens then those 10 posts will just hang out doing nothing on A, but if the user clicks subscribe then A sends another mail to B saying “my user wants to follow poodles.” B replies saying “cool, I’ll send you everything from poodles now.” Now, anything a post or comment happens B checks lots list of subscribing instances and sends copies of them.
If user on A comments on !poodles or posts, it creates it on A but sends a mail to B saying “here is some new stuff for poodles!”