Full Squat! Half Squat!

Full squats are once you perform the full range of motion, when the hips go at the least parallel with the floor (or just below), many people like to go ass to ground (ATG) and that’s fine delivering you have got the flexibility to complete so, if you don’t have the flexibility to go ATG then go as low down as comfortable, so long as its at the very least parallel.
I feel the greatest cause men and women do not carry out full squats is simply because they believe its bad for the knees, sorry to say but this is incorrect, full squats are essentially superior for the knees than half squats and that is due to the fact full squats deliver a full contraction of the hamstrings, glutes and quadriceps muscles, allowing you to drive as much as the start off position working with momentum in the leg muscles and not from the knees.
The full squat must be considered the cornerstone exercise, for the reason that it quickly stimulates overall strength increases in both men and women. Neglecting this exercise retards overall physical development and prevents the athlete from achieving optimal performance. Exercises that use a more complete range of motion at the knee joint may increase rather than decrease knee stability of the medial collateral ligaments and other ligaments.

Half squats are after you stop before your hips are parallel towards the ground. The problem with only performing half a squat is that whenever you drive back up from the bottom of the movement you are not fully activating the hamstrings and gluteus to lift the weight, therefore the momentum of the weight is stopped by the quadriceps and knees, placing undue stresses and shear forces on the knees.
Secondly, due to the fact the hamstrings and glutes are not as involved it causes imbalances between the hamstrings and quadriceps. The hamstrings are supposed to act as the antagonist of the quadriceps during a squat, but due to the fact the hips don't go below parallel this never truly happens. So for those who were to continue training half squats for a period of time you would begin to see muscle imbalances between your quadriceps and hamstrings, which will also reduce your flexibility.
Here is usually a quote about half squats from Dr. Mark Ripptoe: Strong enough, Thoughts from thirty years of barbell training, 2007:
“The fundamental misunderstanding here is about what we’re trying to accomplish when we squat. The quadriceps are not the only muscles that are supposed to be involved inside the exercise. The hamstring muscles on the back of the thigh attach at the front of the tibia, at the bottom of the knee, wrap around it on both sides and pull back on the knee from beneath it as they get tight. The adductors connect the groin area of the pelvis towards the medial (inside) aspect of the femur, and these muscles also pull back on the knee when they tighten, but from above the knee and toward the inside. Both of these muscle groups tighten from behind the knee as the torso leans forward, the knees travel out to stay parallel towards the feet, and the hips reach back of correct depth, balancing the forward pulling stress from the quadriceps and the patellar tendon around the ront of the knee. But they only exert this balancing pull when they are stretched, in the full squat position“
So why would anyone want to carry out half squats? Well half squats can be useful for strengthening your legs at the top of the movement and can really improve strength in your thighs. Also for those who have a sticking point at the top of the movement half squats can really help with this as you can load the bar with a lot more weight.