In a previous page we discussed quadratic and cubic Bezier curves. As you can see above, the cubic form has 2 control points, while the quadratic form only has 1 control point.
The main difference between them is that the quadratic form can only allow a curve in one direction, whereas the cubic form allows curves of many directions.
If you think of the control points as magnets acting on a point moving from the start to the end point, you can see how this would be possible.
Here we are attempting to create a cycloid curve using cubic Bezier curves, and it appears we are very close - the red curve is a true cycloid, while the blue curve is produced by the following path using a cubic Bezier: