I am taking most of the data from Wikipedia here, but most consider this common knowledge anyway.
The BMI or Body Mass Index is calculated by dividing your weight in kilograms by your squared height in meters.
BMI = kg / m²
So for example if you weight 65kg and are 1.73m tall you would get:
65 / 1.73² = 21.7
This index is then matched to a table to give you a rough estimate if you are over or underweight. I copied this table partially from Wikipedia, too.
Very severely underweight less than 15.0
Severely underweight from 15.0 to 16.0
Underweight from 16.0 to 18.5
Normal (healthy weight) from 18.5 to 25
Overweight from 25 to 30
Obese Class I (Moderately obese) from 30 to 35
Obese Class II (Severely obese) from 35 to 40
Obese Class III (Very severely obese) over 40
BMI tables might vary, for example there are other values used for children or even for people from different nations.
These values are, as stated above, only a rough measure, some people with completely good health might fall into the overweight categories easily when they are for example very tall athletes.
BMI is particularly inaccurate for people who are fit or athletic, as the higher muscle mass tends to put them in the overweight category by BMI, even though their body fat percentages frequently fall in the 10–15% category, which is below that of a more sedentary person of average build who has a healthy BMI number.
The Wikipedia article gives a lot of other reasons why BMI is inaccurate for a single person to determine their health. BMI is mostly useful for statistical comparison of groups of people:
The BMI is generally used as a means of correlation between groups related by general mass and can serve as a vague means of estimating adiposity.
Generally, the index is suitable for recognizing trends within sedentary or overweight individuals because there is a smaller margin for errors.