In the earlier seasons of Supernatural (1 through 5), it appeared that when a human dies as a result of physical circumstances, their soul leaves their body and a reaper is there to convince them to come with them. If they go with the reaper, fine. If not, they become ghosts. And there are many reapers who collect the souls of dying people all around the world.
However, come to season 6, in the episode "Appointment in Samarra", Death tells Dean to do his job by wearing his ring and the job is to touch people who are supposed to die (as determined by destiny) and what kills people is the touch of Death. As one dies, one's soul leaves the body and the reapers can collect it.
However, this raises the question: if Death is needed for every death, can Death be at multiple places at the same time? Because clearly, the story has multiple reapers to collect souls all around the world. So, one would imagine that they all need Death to be present with them.
There are also other related questions. For example, the soul of the dead person could see Dean when Dean worked as Death. But when Dean died in season 2 (the episode wherein they first introduced Tessa, the reaper), he didn't see Death. Why the discrepancy?