The art of retouching basically involves removing unwanted items in a photograph or making the existing subject look better. It may just be a bad photograph that needs to look better (color correction) or it may need something added or removed for the sake of making a point or promoting a product.
Retouching many times involves portraits that may not be as good as desired for example an object in the backround is distracting, the person's eyes are red, stray hairs or maybe the person simpy needs to look a little better or younger. (People usually think they look about ten years younger after their portrait is retouched.)

Retouching 1

Retouching 2

Retouching 4