The white meat in poultry, which is found in the breast, is lower in fat and calories then the dark meat in poultry, which is found in the wing, drumstick and thigh.
That's the main reason people pick chicken breast over legs. They are lower in fat and calories.
Also, they're easier to eat. If you buy boneless skinless chicken breast - it's just chicken. You don't have to dissect or pick away at it like you do with a chicken leg.