Classic back and front squats will undoubtedly make you a stronger, more useful human, but at some point you're going to plateau on the amount of weight you can lift. When this happens, you need a little variety to keep the classics working for you. In short, you need this.
Most of us have one leg that's stronger than the other. This is natural, but having too great of a muscular imbalance can cause hip shifting when squatting. This not only leads to an inefficient lift, but also a potentially dangerous situation for your lower back.
Barbell split squats help to work out some muscular imbalances in your lower body since they're a unilateral movement. They're also a fantastic tool to develop balance and coordination between muscle groups.
In the video, I'm using a shortened stance and slight hinge in the hips to emphasize the stress placed on the glutes. Adopt a more upright torso if quad development is the goal.