Most people who start personal training list one of their goals as "weight loss"; this can be achieved in several ways, not all of them healthy.
You can lose lean muscle, fluid or even lop off a limb to "lose weight", but what you really want to do is lose body fat; this is where body composotion is important.
Body composition refers to the amount of body fat you carry versus everything else that isn't fat, like lean muscle, organs & body fluids.
A healthy body fat percentage for women is between 18% and 28%, for men it is 10% - 18% and knowing your body composition allows you eat well to maintain your lean body weight and improve your body's fat burning potential.
The data below explains the difference between two people who 'weigh' the same, but with different body composition and activity levels:
Body weight 60kg
Body fat 10%
Fat weight 6kg
Lean weight 54kg
Body weight 60kg
Body fat% 30%
Fat weight 18kg
Lean weight 42kg
*Basal Metabolic Rate (how many calories you burn just keeping your body going) + Activity = Total calories needed to maintain your current weight.
So you can see that despite weighing the same number, the body composition (lean weight vs fat) of Person A allows them to consume more than twice the number of calories as Person B, and given their body fat %, it's a safe bet that more of their intake is nutrient rich food.
I advise all of my clients with fat-loss goals to get their body burning body fat reserves as fuel while building and maintaining lean muscle; the same amount of muscle weighs more than fat, so they may not initially see a drastic reduction on the scales, but you will see and feel your clothes getting larger without feeling deprived of tasty & nutritious foods.
Eating lean protein and as many vegetables as you can with every meal, avoiding processed foods and getting in 30 minutes of cardiovascular work each day, as well as 3 - 4weekly weight sessions will see you gradually and safely reaching your goal.