B-spline Curve Order
In practical terms, a B-spline curve's order defines the curve's distance from the control polygon's poles. The greater the order, the further the curve can lie from the poles of its control polygon. A high-order curve is "freer" than a low-order curve.
The limit to a curve's order is the number of poles: You cannot place a B-spline curve with a greater order than the number of poles.