After doing strength training, the body's levels of Human Growth Hormones rise, and tend to stay elevated for approximately 48 hours. During this time your body sees the most muscle growth. So bodybuilders tend to tried to schedule a major strength training session every 48 hours to keep the Growth Hormone levels continuously high.
Additionally, to achieve maximum growth a muscle needs some time to rest, as strength gains are made during recovery.
That being said, for most of us who are mostly trying to improve overall fitness, having a cardio exercise that happens to work the same muscles on the off days should not hurt you, and probably will help reduce Delayed On-Set Muscle Soreness. Just make sure that you occasionally have a complete rest day to allow for fuller recovery.