The BMI is a convenient, and simple way to classify a person based on their weight and height. Major BMI classifications are underweight (under 18.5 kg/m2), normal (18.5 to 24.9), overweight (25 to 29.9), and obese (30 or more). It is used to predict a person's health, the further you are away from the normal range, the greater the health risk.
Although BMI is not perfect, it's simplicity means it is widely used.
It is important in climbing, because there is no doubt that as a general rule, the lower your BMI, the easier it is to climb the harder routes. This is not without it's dangers, in particular competition climbers will diet to reduce their BMI, and this has led to many eating disorder issues. As a result the IFSC sets guidelines that climbers should not have a BMI less than 18 to 19.