The Silver Key is an object found in the dresser drawer of Sans's room. It is used to unlock Sans's workshop, located in the back side of his house.
The Silver Key can be acquired only in the Neutral Route if the protagonist gained no EXP, as entering Sans's room is needed to obtain it. To get the key to his room, the protagonist must save, reload and talk to him again in the Last Corridor.
The fact that this key is explicitly silver may allude to H.P. Lovecraft's short story "The Silver Key", which focuses on time travel.