This is a parametrized, animated Spirograph. The parameters can be manipulated by dragging the three dots. (Before manipulating points, the animation has to be stopped with a double click.) A Spirograph is the curve traced by a fixed point on a circle rolling inside a fixed circle. (This is more or less a defintion by Eric W. Weisstein.)
The LiveGraphics3D programming is not perfectly trivial in this case, but most of it is described on this page.