There are two distinctive features of a
weightlifter's body: one is the well-developed
trapezius muscles, which they get from the pulling in the
snatch and
clean-and-jerk. They are also known for having tree trunks for legs, or very large
quadriceps from front squatting.
One day I will be freakish in both these respects and then
you're all fucked.
Most weightlifters both front and back squat, but in terms of priority, the front squat is usually the assistance movement of choice. The difference between the two movements is subtle, but enough to warrant favoring one over the other. In the back squat, the bar rests across the trapezius muscles; in the front squat, the bar rests across the collar and shoulders. This shifts the athlete's center of mass, and therefore changes the stress of the weight and the leverage. With the bar's weight slightly ahead of the center of mass, the torso must be kept much more upright than in the back squat; this emphasizes the quadriceps muscles intensely. In the back squat, the lifter can afford some forward tilting of the torso, allowing the glutes and hamstrings to play a larger role in moving the weight. Also, in the front squat, the base of support (the trunk) is less stable because there are more "links in the chain" (the shoulders and collar hold the bar, employing "pulling" muscles in the back - lats, rhomboids, etc. to establish a shelf, all the while maintaining an erect torso with the abdominal and lower back muscles; in the back squat, the bar is directly aligned with the hips and rests upon the actual spine instead of extensions of the spine).
The front squat is more difficult than the back squat, so why train it?
For weightlifters, the answer lies in specificity; the front squat more closely emulates the bottom receiving position of the squat clean, meaning that if the front squat goes up, the clean should follow suit, or at least the recovery from the clean should become a little easier.
Some strength and conditioning coaches have begun to favor the front squat over the back squat because it is more difficult. Since it requires strict form and a tight, erect trunk, they believe it's a more efficient lower body strength-builder than the back squat, because of the greater emphasis on the quadriceps, allowing there to be a clear division between lower body "squatting" (quad-dominant exercises) and lower body "pulling" (hamstring/glute/lower back exercises), and because they feel it's safer; an athlete can muscle out a back squat with bad form, risking the ever-worrisome lumbar injury, but anyone who tries to front squat without an erect torso is probably going to be forced to dump the bar.
From a bodybuilding perspective, the front squat may be favored in some cases because, again, it allows for a greater emphasis on quadriceps development than the more general training effect of the back squat.
Since the movements are similar, there is some correlation between how much an individual can back squat and how much he can front squat, generally around 80-85% for individuals who train both; their best front squat for a single is about 80-85% of their best back squat for a single. However, it is not uncommon for some athletes (i.e. weightlifters who emphasize specificity) to front squat more than they back squat (I am on the verge of becoming one of those weightlifters) because in certain phases of training the back squat is almost completely excluded.
Is the front squat necessarily a superior movement compared to the back squat? Probably not. In terms of building strength, the back squat is irreplaceable. Nothing else will develop lower body strength as well as ground zero back squats, and those still establishing strength foundations would benefit more from focusing their efforts on the back squat and using the front squat merely as assistance work saved for a lighter day or a change in habit. But if you want bigger quads, a stronger clean, or a tough alternative to an already tough movement, front squats are your thing, my friend.
You can front squat the same way you back squat, go for a max single, a set of 10, a set of 20 if you are so inclined, but it might take a little work to get there. A lot of people have trouble with the flexibility component of the movement, the rack position with the elbows up and wrists hyper-extended, but it comes with time as long as you're sufficiently young. It took me months before I could get comfortable with the rack position. You can go for the arms-crossed rack, where your arms are crossed in front of you, but in my opinion this kills the shelf; clean-grip is the best way to go.
Donald Shankle, currently the US's top-ranked 105kg lifter, is an example of an athlete who benefits from nearly exclusive front squatting. His best clean-and-jerk is something like 202.5kg, 445.5lbs, meaning his best front squat is ten or twenty kilos heavier than that. His coach explains that his base of strength has been developed to the point that back squatting now gives diminishing returns in terms of its worth; at this stage, Shankle merely trains the back squat as "maintenance" work, rather than attempting to post higher numbers in training. The role of "active" assistance work has now been shifted to his front squatting, in order to improve his clean-and-jerk. Frequent back squatting would be detrimental to his training because the recovery time it requires would hurt his performance in more specific movements.