Note that the Earth, society, etc is all completely the same if that matters at all.
I find it difficult to believe that a society of indestructible immortals could be remotely the same as any current human society. Do they at least feel discomfort? For if they don't, then a lot of things we take for granted - not simply hospitals and cemeteries - become pointless. If people can't die for any reason, included starvation, this means they don't need sustenance. Do they still enjoy food?
Having infinite time to do anything isn't really likely to go hand in hand with today's society's hectic pace. Also, people have time to do everything - learn a lot of different things, practice different crafts.
If people still get born, as it seems, then this one mortal might well find himself in a lethal environment from the beginning, because everyone else knows no better. All newborns are kept at a balmy -40 °C: it is so convenient to have certain... substances freeze solid almost at once, becoming easily disposable, and it inconveniences the little darlings not at all!
If the guy becomes mortal (or discovers his mortality) later on... this scenario is presented in Damon Knight's The Dying Man (1957) (available here).
"Something's the matter with it," is all she can find to say.
"Yes. It's dying. That means to cease living: to stop. Not to be any
"No," she breathes. In the box, the small body has stopped moving. The
mouth is stiffly open, the lip drawn back from the yellow teeth. The
eye does not move, but glares up sightless.
"That's all," says her companion, taking the box back. "No more rat.
Finished. After a while it begins to decompose and make a bad smell,
and a while after that, there's nothing left but bones. And that has
happened to every rat that was ever born."
"I don't believe you," she says. "It isn't like that; I never heard of
such a thing."
How would people react. Incredulity, as above. Very possibly fear. More or less rational fear of contagion, and desire to destroy the monster. Pity. Scientifically minded immortals would want to examine the creature to determine the differences; what it is that makes it immortal.
It might even be the case that for some individuals he might become a prophet, a dream, a hope - the hope of finally freeing themselves of a life became unbearable because of boredom, ennui, guilt or whatever. Being immortal means that it never stops, even if you don't like it. A religion might spring up promising at last the blessed oblivion of Death.
How can they be so much immortal?
The above holds imagining that really they can't die in any way, which is implausible; a sufficiently high temperature will convert their very matter to dispersible plasma.
Which means that to be able to survive, they need to be not made of matter.
So, they might be simulated beings in a computerised Earth-analogue, and the mortal one could have caught a bug. (pun possibly intended)