Execution:

The front squat requires the exact same range of motion as the air squat. The foundation of this movement is identical. The start and end points are achieved when the hips, knees and shoulders are in one straight line and the movement has been successful when the bottom position has the crease of the hip lower than the knees.
However in this movement you have a barbell in the front rack position. The front rack is attained with the barbell resting on the clavicle and deltoids, elbows high and ideally all the fingers around the bar.
Maintaining a good front rack position through the squat is crucial for a solid front squat. This requires good mobility through the chest and strength through the lats and core. As the squat is performed, the elbows must remain high and chest tall. At the bottom of the squat the elbows must not make contact with the knees.

Purpose:

The front squat develops core, trunk and back strength as well as improving mobility. It improves squatting strength and is an important movement to help with the clean. It also improves quad strength which can help develop the jerk.

Programming:

The front squat can be programmed both as part of a wod; from either the floor (which requires the barbell to be cleaned) or from the rack, or it can make up part of the strength program.
Rep ranges, weights and sets can vary depending on the situation. Generally the reps and weight in a wod will be higher and lower respectively. Conversely the weights during the strength program will likely be a lot heavier and reps and sets lower.

Variations:

Front squat variations include pause or tempo front squats as well as 1 ¼ squats. Front squats can also be performed with dumbbells or kettlebells.