The air squat, or more commonly known as just the squat, is a variation of the load bearing squat. In this instance the squat, which is a powerful tool in building lower body strength, pliability, and endurance, will be explained in some detail.
There are some beginner ways to start building lower body strength for those not yet capable of performing a squat. Some of these ways include exercises altogether different from the squat, yet still function in strengthening the thighs enough for a squat. It is, however, enough to be able to sit and stand. That's pretty close to a squat already.
So, if it is necessary, one may do squats over a low bench. This allows the feet to spread shoulder width apart and the body is lowered by bending the knees. The back is kept as straight as possible. (Looking at the ceiling can help this action)
Having the bench beneath the person allows the glutes to touch the bench in the event that the person's lower body is under developed. After a few weeks of 3 sets of 10 of these squats every other day the lower body should be strong enough to do squats safely without the bench/stool/cushions or whatever is used.
Aside from building strength, the squat tones several muscles in the lower body including glutes, hamstrings, quads, some of the lower back groups like the erector spinae, and even the abs when the entire core is held firmly.
It is important to remember that not everyone is a body builder. There isn't always a need to load 225 pounds on a barbell and do power squats. Several sets of several controlled repetitions without weights combined with different foot positions can truly build a great lower body. This especially true when the horse squat is performed slowly.
This variation not only tones the thighs and buns, but also opens the hip joints. A narrow stance (the feet closer than shoulders width apart) tends to hone in on the vastus medialis muscles and the vastus lateralis muscles. The squat is truly a versatile tool for your lower body arsenal.
There are many different ways to take advantage of this amazing exercise. Be extra careful to never jerk up or down quickly as this may cause undue stress on the knees. Slow movements always beat out fast repetitions when training for endurance.
Here are some videos on squat variations.
Always consult your physician before starting a new exercise.