I hope you have made fitness a habit and are working out almost every day. Notice I said almost every day? Rest days are an important part of your fitness program.
When strength training you are actually tearing your muscles and when they rebuild is when they get stronger. That is why you shouldn't work the same muscle group with any type of resistance on back to back days. You can work different muscle groups on different days to help with muscle recovery. For example, upper body one day and legs the next.
Rest days are still important even when splitting up days to weight train muscle groups. Exercise, especially higher intensity workouts, are taxing on your body and deplete your glycogen stores which you use for energy. In order to keep progressing, and reduce your likelihood of injury, you need to give your body a break once and awhile to repair and re-energize.
So how often should you rest? If you are starting out with a new exercise program or are a beginner exerciser, rest every third day (that is, exercise two consecutive days and rest the third). More experienced exercisers should remain inactive or take an active recovery day once a week.
What does a rest day look like? How inactive you are on your rest day depends on the intensity of your workouts leading up to it. For example, if you are killing it in the gym day in and day out, your rest day should be a day completely off, maybe go for a walk, but no gym or workout video. However, if your workouts have been light to moderate intensity all week, you can take a more active recovery day. That might include playing a sport outside, taking a yoga class, or going for a longer walk.