The parallel front squat is a partial squat to strengthen the most mechanically weak position in the squat to help lifters move through their sticking points more easily. The front squat variation will transfer more directly to clean recoveries than the back squat because of the same posture and the greater emphasis on trunk strength.
 
Front squat as usual but stop when the thighs are approximately horizontal—just look for the position you want to stop in least, and stop there. It may be slightly above or below horizontal. Stand again without continuing lower.
 
The key is ensuring your position is correct—the tendency will be to sit the hips back and shift to the heels more to make the position easier, but this defeats the purpose. Likewise, fight to maintain the upright posture as you recover rather than leaning forward and pushing the hips back.
  Notes
This variation places more strain on the knees than full-depth squats for athletes with adequate mobility, so only use it if you have healthy knees and plan to take care of yourself.
 
Purpose
The parallel front squat forces the lifter to stop and change directions at the most mechanically disadvantaged point in the movement, where the leverage is the worst. This will build strength in this position, which can help lifters improve their ability to drive through the sticking points of their cleans and squats.
 
Programming
There are a number of possibilities when it comes to programming the parallel front squat. Most common will be sets of 3-6 reps and using this variation as one of 2-3 or more squat sessions each week. It can also be used for back-off sets following sets of full-depth front squats.  
 
Variations
The parallel front squat can be performed with a pause at parallel, or with prescribe tempos in one or more phases.