Definition:
A Claude Mirror is a convex mirror with black on the back rather than silver. It reduces the quality of the reflected image, producing a softer, muted effect which makes it easier to see tones in a scene (and thus, in theory, easier to paint). The convex shape of the mirror means it reflects a larger section of landscape than you'd see normally.
Try looking at a scene reflected in a convex mirror (a make-up mirror, or a car mirror for reducing blind spots) through a pair of dark sunglasses and you'll get a similar effect. Like other optical devices, the Claude Mirror has been replaced by photography, as it's easy to manipulate a photo to reveal tones.
The mirror is said to be named after the 17th century French artist Claude Lorrain.