Pillow shading is method of "shading" artwork, typically employed by novice pixel artists. It adds lighting to an image, though as seen by many, the "wrong sort" of lighting.
Pillow shading generally involves creating a gradient leading from the outer edges of the image to the center. Though it can be dark-to-light, light-to-dark variations are the most common, giving the impression of a "pillow" - a flat, unrealistic interpretation of the object, in which the light appears to be coming from its center.
It is a common misconception that pillow shading is a concept not used in video games, however, most rounded lights employ pillow shading such as energy projectiles in action shooters (e.g. Mega Man). However, if the light is not coming from the center of the object (or being shone at the object from the Z direction), it is usually frowned upon by artists.