Wide stance squats hit more of the inner angle of the quadriceps as well as the middle glutes. For TKD athletes, this is mostly important for longevity because inner quads stabilize hip and knee joints against all the conditioning work necessary for the outer hips and glutes.
Hold a kettlebell or whatever weight you choose and set your feet wider than hip width. Angle the feet slightly outwards and keep the knees squeezed out to angle over the feet without tipping inwards. Fold at ankles, knees, and hips to squat, not allowing the knees to pass beyond the toes.