Control handles located at the control points determine the shape of the curve in each section, and work much like an elastic band. Forgive me the steady motion on the image at the left, but this is one action that is so much easier to show than to put into words. As you move the control handles, the shape of the curve section changes, which is the most wonderful and the most confusing part of bezier curves. Lines do not have control handles, because only the end points can be moved. Obviously, if the line could curve, it would not be a line.
Curves are the most versatile bezier section type.
The control points in bezier curves can also be set to different types. In illustration programs you can set the points to allow the curves on each side of the control point to act independently, or symmetrically or to act independently but maintain a smooth transition over the control point. The sample images at the left provide an illustration of various bezier control point types. Note how the symmetric sample maintains a gentle curve on either side of the control point. The smooth sample allows the curve to vary dramatically on either side of the control point, but keeps the transition across the control point very smooth.