Doh ever say Afro Chic didn't teach yuh anything...
From Yahoo! Answers.
It means you are relying on previous accolades or successes.
Laurels were once given as an honour for achievement--think of Roman senators wearing crowns of laurels. One who "rests on his laurels" is content with present, or past achievements. Though laurels are positive, one who rests on them is considered lazy.