Any closed curve can be decomposed into a sum of rotating circles at different frequencies. The Discrete Fourier Transform finds the amplitude and phase of each frequency component.
The DFT treats the drawn path as a discrete signal sampled at N points. Each frequency component k corresponds to a circle rotating k times per cycle. The amplitude sets the circle's radius; the phase sets its starting angle.
Low frequencies capture the shape's overall structure. High frequencies add fine detail and sharp corners. More terms means more circles and a closer approximation.
The reconstruction is exact when all N terms are used because the DFT is invertible. With enough epicycles the traced path converges perfectly to your original drawing.
Jez Swanson, interactive · Wikipedia