The order of the curve is related to the least points used when defining the curve, that is, the order of the curve = the least points used when defining the curve-1.
That is, a straight line is 1 order (2 points-1), a parabola and an arc are of order 2 (3 points-1), a free curve is of order 3 (4 points-1), and a complex free curve may be of order 4 or more (Rhino has a highest value, which seems to be as high as several tens, generally).