Quads, glutes, and entire lower body
This is a great way to ensure you're achieving a uniform depth with every squat. It also provides some security for people who feel they need it. You know you're not going to fall or not be able to get back up because the chair is right there.
Stand a few inches in front of a sturdy chair (or further if needed - adjust yourself accordingly). Bend your knees and reach your hips back like you're reaching your butt towards the chair keeping your knees behind your toes the entire time. Drop down to chair height, touch lightly, then return to standing. Use your core throughout to maintain good upper body posture (don't slouch!).
Make it easier:
Start with a taller chair and/or don't reach all the way to the chair and/or rest longer between reps.
Make it harder:
Use a lower chair/surface to squat to and/or hold some manner of weights in your hands or to your chest.