"Smart stay" is a feature on the Galaxy S4 that senses when the user is looking at the phone's screen. This allows the device screen to stay lit even while the user is not physically touching the screen, and timeout correctly when the user does not look at the screen.
Smart stay is a mode enabled in the settings of most Galaxy Android phones and is found in the display category. Developed originally for the Galaxy S3, the setting allows the phone to periodically check the camera to determine if the user is looking at the screen. This prevents the phone's screen from timing out improperly by using the camera if the device hasn't registered the user's touch.