fedia.io is a specific "provider" in this context. fedia.io runs on mbin. Lemmy is analogous to mbin. Many "providers" run on lemmy: lemmy.world, lemmy.dbzer0.com, lemmy.wtf, etc.
What is being provided is fediverse access. "Fediverse" is not my mostest favorite term, but it's the one that's most accurate.
Since you're on fedia.io, which runs mbin, I can answer some of that for you.
Under a post (or a comment for that matter) there is a "More" link. "Open original URL" will open a new tab of that post or comment at the instance the user the post or comment was from.
So if I Open original URL on this post, it will open a new tab at fedia.io for this post - because you posted it, and you posted it from your fedia.io account, at that instance.
However, if I Open original URL for the comment by @meldrik@lemmy.wtf a new tab will open of that comment in this post at lemmy.wtf.
That's how that function works, but the reasons you'd actually want to do it are limited. Perhaps the instance you're viewing the post through is defederated from some other instance, and so you wouldn't see comments from users at that instance. Opening the post "somewhere else" that wasn't defederated from the instance you wanted to see comments from would then let you see them - but not interact there, unless you also had an account at that instance.
So far as I know, fedia.io is only defederated from a very small number of tankie-heavy instances (lemmy.ml and hexbear/chapo.chat are the ones that come to mind). I don't think the thing you are asking about doing really has a use case.
Isn't it amazing that these "paragons of business" failed to recognize that Little t would be bad for their bottom line in October 2024? Because I sure the fuck did, and I am no "paragon of business."
https://youtu.be/nWwKJxCa_Ao
Notable points: