The Doors of Death are the personal gateways used by the death god Thanatos' to enter and exit the Underworld. During most of the events of The Heroes of Olympus, Gaea has control of them, but ownership is returned to Thanatos in The House of Hades.
Much like how people can pass into Olympus using a magic elevator, the Doors of Death also appear as an elevator in and out of the Underworld. However unlike the elevator to Olympus, the Doors of Death are framed in Stygian Iron, with black and silver doors etched with art deco designs, making them a complete inversion of the Olympian doors.
The Doors of Death act as a fast passage in and out of the Underworld for Thanatos, who is in control of bring people to the Underworld, as well as making sure that no one ever escapes as well. Also Thanatos is able to tell where the Doors of Death are at all times, even if they are not under his control. According to Bob, when the Doors are not chained, they move around after use which keeps them from being found and under Thanatos' control.
When the Doors of Death were in the possession of Gaea, she forced them open while Thanatos was captured and allowed monsters and evil souls to escape the pits of Tartarus in order to help her in her quest to destroy the Olympians and their children. In order to prevent Thanatos from simply moving them, they were chained in place. Also, in order for someone to pass from Tartarus into the mortal world, someone would have to hold the button for 12 minutes and someone else would have to hit the button on the mortal side, or else anything in the elevator would simply vanish. The Underworld side of the Doors were chained in the heart of Tartarus while the mortal world side of the Doors were chained in the House of Hades. Both locations were heavily guarded and both sides of the Doors needed to be freed in order for the Doors to reset. With the Doors in Tartarus, it was considered impossible to free them as no demigod could survive Tartarus and no god, not even Thanatos himself would go there.