I usually hear it as "There's no rest for the wicked", but your version is common as well. It's from the Bible. It's often used in a humorous way nowadays. This site gives a more detailed explanation: http://www.phrases.org.uk/meanings/257500.html

Weird, italki edited out my bracketed line. It originally said " **Night shift worker arrives at work. Early shift worker is still there...** " (Then the example phrase)

Regarding usage - precisely as Susan says, it is commonly, "No rest...". In my (Brit.) experience, it is never used in a serious manner, only for "mild comic effect" as Susan's link explains. E.g. <Night shift worker arrives at work. Early shift worker is still there...> -"Hey, shouldn't you have left an hour ago?!" -"Yeah. I know. No rest for the wicked..."

It simply means that "If you are Bad person there will be can't have PEACE of mind".

It is like saying there is nothing good for bad people. No peace = peace as in peace of mind (their minds will always worry, be in turmoil, etc) Wicked = bad people, mean people, etc,