The band resisted split squat can serve a few purposes:
1) The band resistance just above the knee makes the glute muscles on that side work harder during the split squat exercises.
This is great if you're putting an emphasis on training the butt muscles a bit more during leg exercises.
2) It can be a useful corrective strategy. For many people, when they do leg exercises such as split squats, lunges, squats, and deadlifts, you sometimes see one or both knees drop inwards. Something called valgus collapse.
Pressing the knee into the band throughout the exercise teaches correct positioning which should reduce the amount of collapse.
• Attach a resistance band to a solid object and place around the leg that will be in front
• Stand tall with abdominals braced. Arms by sides. Sideways to bands point of attachment
• Take a large step forward into a staggered stance. Back leg is straight with heel off floor. This is the start position. Front leg should be the leg furthest from the point of attachment
• Keep torso upright or in a slight forward lean, bend both knees and lower hips straight down towards floor.
• Lower until knees are bent approximately 90 degrees but stop before back knee touches floor.
• To reverse, press front heel into floor and squeeze butt muscles to raise hips straight up and return to start position.
• Repeat all reps on one leg before repeating on opposite side.
This is my, mostly, Personal Trainer musings and information which I hope you'll find helpful!