The terminology is that you federate with an instance and subscribe to a community.
And yes, if you sub a community, your instance will mirror posts and comments to your local DB and re-serve them to the public unauthenticated internet. On a single-user instance, anyone can browse the communities on your server and infer what your account subscribes to, including whatever porn, piracy, and other legally questionable shenanigans based on what gets replicated to your server.