The Squat is a functional movement
The term functional training is very common these days. Functional training is typically perceived as a modality of training that crosses over to real life performance. An example would be, if you are great at doing walking lunges you should therefore assume that your gait cycle (walking pattern) will also be competent and skilled. The squat targets the posterior part of the body (posterior chain) i.e. the spinal erectors, glutes, hamstrings and calves. By stimulating these muscles, we develop better strength, mobility and movement patterns.
Losing fat and gaining muscle
When perfoming the squat we stress our body greatly, mostly because of the sheer amount of muscles that have to work in synergy to enable us to perform the movement efficiently and effectively. This type of exercise can be categorised as a compound exercise. When training we typically do compound or isolation exercises. Compound exercises work multiple joints at any given time and isolation exercises work a single joint at a time. When looking at the effectiveness of these to types of movement its not hard to see what one is going to do the most for you in terms of fat loss and body composition.
Mobility and flexibility are two different things. Flexibility is your muscles ability to passively lengthen through a desired range of movement. Mobility is the ability to move a joint actively through the desired range of movement. Flexibilty looks the length of the muscle so that means if it tightens up you might just be short of being able to touch your toes. Mobility takes a more global approach, looking at the nervous system, the joint, its capsule and any muscles that cross it. In the case of the squat this relates to the musculature of the hips. If you have spent years trying to touch your toes but to no avail then perhaps through diligent programming of your nervous system you can enhance mobility and simultaneously improve the squat.
General Physical Preparedness
SAID principle ( Specific Adaptations by Imposed Demands) talks about how you will get what you train for. So in respect of the squat, if you train for a better squat, provided all the variables are addressed properly, you will get a better squat.The squat has tons of transferability to other movements and exercises, thus improving your general physical preparedness. Improved General physical preparedness means that you are opening the door to loads of more complex movements and in fur will mean that you get far better returns in your physical development.