Daily rest will do more to determine how you will respond to your training than any thing else. Get enough rest (7-9 hours for most) on a daily basis and you will improve. Get insufficient or inconsistent sleep and you will get injured, burned out or see no results from your training.
Recovery days are required between intense workouts. The more intense the workout, the more recovery you need before the next intense workout.
You also must plan correct rest between intervals. The amount of rest you get determines the response you will get from the interval. Alactic anaerobic intervals require a 10:1 rest to work ration for all out intervals. Anaerobic intervals require a 3-5:1 rest to work ratio. Aerobic intervals require a 1:1 ratio or less.
Recovery weeks are require during a training phase. You can not just keep adding intensity or miles. Minimum is a recovery week after 3 weeks of training. Higher intensity or volume may require a recover week after 2 weeks. Very high intensity or training may require a recovery week after just 1 week.
Finally you need a recovery phase after your competitive race phase. This should be 2-4 weeks of very light workouts to stay in shape, but let the body totally recover.