How much cycling distance is needed to travel every day for good muscular exercise?
As individual speeds vary depending on fitness, bike and conditions, most information on this subject discusses intensity and time spend exercising, rather than distance. Most leisure cyclists ride between 10-18mph (16-30kph) on the road, a bit less off-road. As you can see it's a fairly wide range, so time and intensity are better measures.They can also more easily be applied to other sports. 

For good health, the WHO recommends:


  Adults aged 18–64 should do at least 150 minutes of moderate-intensity
  aerobic physical activity throughout the week or do at least 75
  minutes of vigorous-intensity aerobic physical activity throughout the
  week.


If you'd like to improve your cycling fitness as well as your health, then British Cycling has a number of beginners training plans, depending on what you would like to achieve.

However, not everyone responds the same way to exercise, so the improvements are not guaranteed.