The Body Mass Index (BMI) is a number which is calculated by

It measures the relationship between your height and weight and provides an estimate of the amount of body fat.
The BMI for children and adults are calculated the same way. However, they are interpreted differently.
As children grow, the amount of body fat changes with age so BMI for children needs to be interpreted in relation to a child's age. There are also gender differences. Therefore, for children and youth, BMI is age and gender specific. This means that the age and gender of a child must be considered when interpreting their BMI.
Once the BMI value has been calculated, it is plotted on a BMI-for-age Percentile chart. Separate charts are used for boys and girls.
BMI-for-age Percentile Chart, Girls, 6 - 18 years
BMI-for-age Percentile Chart, Boys, 6 - 18 years
When the BMI (vertical axis) is plotted against the age (horizontal axis), it intersects to show which percentile or percentile range that particular BMI value falls within. See example here.
Different percentiles or percentile ranges indicate different weight categories.

The percentile or percentile range shows the relative position of the child's BMI among children of the same age and gender.
For children, BMI is used to determine if they are severely overweight, overweight, of acceptable weight, underweight or severely underweight. It is not a diagnostic tool. So, if you find that your child is overweight, it is best for you to consult your doctor to find out if he/she has any health problems associated with his/her weight.