It's the replacement word for retarded, because retarded is an insult to people who have mental retardation. People who are actually retarded feel sad when people use this word to tell others that they are stupid or dumb. So, by using contarded, you wil not insult other people.
"Hey Joe Ike, i thought that hannah montana and miley cyrus were two different people!."
"Ugh, Ricardo! you are so contarded!"