Retarded is a word to describe someone who is mentally slow. This is a medical word that spread to slang, and is today considered very insulting and inappropriate.
Some uses of retarded are harmless, like if you said wearing a backpack retarded or slowed down your progress on a hike. However, if you use retarded to mean stupid, you're on dangerous ground. Out of respect for people who have clinical mental retardation, this is considered an offensive term to throw around.