Reapers are undead humans, who remain on earth in an official capacity to help dying individuals "move on." It's treated as a public service and an act of compassion by Rube, the leader of this local cell of Reapers, who explains that the taking of the soul before death spares the soul of experiencing the trauma of actually dying.
Reapers take the soul by physically touching the decedent, either before or right after death. George is initiated into Reaperhood when she dies, as another Reaper passes the mantle on to her when he takes her soul in his last Reap. Reapers do not know when they will pass on, until their very last reap. Reapers are not invulnerable, but heal or repair themselves quickly - they cannot (in theory) be killed again.
Daily, Rube receives his team's assignments from an unnamed and unseen deliverer, and he then transcribes them onto yellow sticky notes to give to his charges. The slips only contain the first and middle initials of the decedent, last name, location and estimated time of death, forcing Reapers to be creative when finding their decedents in time.
Reapers are organized into groups by types of death: Rube and his club are responsible for reaping those who've died from artificial means such as accidents, suicides and homicides. Other groups of Reapers are responsible for deaths due to plague and another old friend of Rube's is implied to be a former reaper for those who die of old age.