First of all it isn't fixed numbers. It is a range. In a non Diabetic the normal range blood sugar levels will vary since the amount of glucose in an individual's blood varies due to several factors, these ranges are simply acceptable levels.
For most normal (non-diabetic) individuals, normal glucose level means a blood sugar concentration of around 6 mmol/l and above around 4 mmol/l measured about 2 hours after a meal.
These people will also have readings of 3.8 - 5.5 mmol/l fasting blood glucose level. This is usually measured 6-8 hours after your last meal. Again, it all depends on your own 'normal' levels and circumstances, foods, timings, conditions.....there are so many variables. The numbers are also different when you look at different reference books and laboratory ranges. All I will say is that if you are around those levels then I personaly wouldn't worry about them.
Ken