Just like a traditional squat, a single leg squat works the glutes, hamstrings, quads and abdominals, however the single leg squat has the added challenge of balance which can also help you to engage your core muscles.
There are several progressions of the Single Leg Squat:
Option 1: The most basic single leg squat can be done by placing a block or a chair behind you, finding your balance on one leg and slowly lowering yourself down onto the block or chair. You can then stand back up using both legs.
Option 2: A little extra challenge would be to remain on one leg throughout the movement and continuing to stand up on one leg.
Option 3: A more advanced movement if you would like to increase the challenge further is to do the exercise with a lower block. This can be achieved by getting a lower block or raising yourself up in comparison to your bock, for example by standing on a weight plate, or a pile of large books/magazines.
Option 4: The final level to this movement is to perform the exercise with no block whatsoever.
It is best not to progress onto a more challenging movement until you have mastered the basics, as doing challenging exercises with bad form is less productive than doing easier exercises with proper form.