BMI or Body Mass Index is the ratio of height and weight. the range for normal BMI is 18-23. If your BMI is less than 18 you are underweight and need to gain some weight. If your BMI is more than 23 you are over weight and need to lose your weight.
BMR or Basal Metabolic Rate is the rate at which your body burns calories in 24 hours. It differs from person to person. The more your BMR means your bodies calorie needs are more and you will tend to lose weight faster. You can boost your metabolism by eating a balanced diet and doing regular exercise.