The Grim Reaper's office is where a player goes the first time they die. From here, the Grim Reaper tells the player about in-game death, respawn points, and gravestones. Once you leave the office, you return to Lumbridge and the gravestone timer starts.
There is a minor glitch where, as the player enters the Grim Reaper's office, he/she appears to have all of their items equipped.
If you try to open the world map in his room, it says "It would be unwise to open the world map in Death's realm."
In his room when you first die you keep equipment worn on death worn, implying the death hasn't or doesn't register until you leave the area.