Reapers are pure souls.
Their soul flames are the strongest, purest colours, represented by the shade of their hair. They are immortal. Only they can see living souls, so it's their job to collect them when the time comes.
As a reaper, it is vital that one shares no emotions or attachments with a living. Acting upon emotion when reaping results in loss of reaping power and ban to mortal life.
Rei is a reaper who acts on his heart.