

Maybe Lemmy is a 2020s version of phpBB (the forum software, which is open source like Lemmy is). Lemmy and phpBB can both be hosted by anyone, but of course the interesting thing about Lemmy is that Lemmy servers can share their content with each other.
I don’t know about the apps because I normally use Lemmy on the web. There might be an option in your app to just see posts from your subscribed communities though.
On the Lemmy.world website you can see posts from your subscribed communities by clicking the “subscribed” tab near the top of the page (the other tabs are “local” which shows you just posts from your instance - Lemmy.world in your case - and “all” which shows you the top posts from all Lemmy servers).
Also on the Lemmy.world website, if you scroll down on the main page, you can see your subscribed communities in a list on the right-hand side of the page. I sometimes use that list when I want to look at a particular community.