From A Wiki of Ice and Fire
The Moon Door is a narrow weirwood door that stands between two slender pillars in the High Hall of the Eyrie. A crescent moon is carved into the door. Across the door are heavy bronze bars that bar the door, which opens inward. The door opens into the sky and a six hundred foot drop to the stones of the valley below. Most executions at the Eyrie use this door.
A Game of Thrones
A Storm of Swords
After chastising Sansa Stark for kissing Petyr "Littlefinger" Baelish, Lysa Tully grabs Sansa and drags her before the Moon Door. Lysa pushes Sansa closer and closer to the edge, until Littlefinger arrives and tells his new wife to release her. Petyr promises never to leave her side again, and as his wife falls into his arms, he tells her he has only ever loved one woman, Cat- and then shoves Lysa out the Moon Door.