In preparation for fighting the Silence, a race of aliens with the power to erase themselves from the memories of all who encountered them, the Doctor implanted nano-recorders into the palms of Amy Pond, Rory Williams, River Song, Canton Everett Delaware III, and himself with a pistol-like injector.
When activated by the user pressing on their palm, the device recorded all the user's speech via a telepathic link attuned to the speech centres of the user's brain. In this way, when one of the TARDIS crew encountered the Silence, they could describe the encounter aloud and record it to their nano-recorder. The nano-recorder then glowed with a pulsing red light to indicate it had been used. Afterward, when the user had forgotten the encounter had happened, they would be alerted to it by their glowing palm. They could then activate the nano-recorder again to play back their own message.
When the Silence abducted Amy, they removed her nano-recorder and left it behind. Rory found the device, which had defaulted to live mode, allowing him to hear Amy's speech live via the still-functioning telepathic link.
Behind the scenes Edit
"The Doctor's Nano-recorder" (more accurately, the injector pistol which implants nano-recorders) was released as a toy by Character Options.