The Radius allows you to directly control the width of the extrusion along the “spinal” curve. The Radius of the points is set using the Shrink/Fatten Radius transform tool Alt-S, the, or the .
Remember, these curves can be converted into meshes with Alt-C in Object Mode.
This setting controls how the normals (visualization: arrows) twist around each control point – so it is only relevant with 3D curves! You set it using the Tilt transform tool in the Tool Shelf, the, .
You can also reset it to its default value (i.e. perpendicular to the original curve plane) with Alt-T,. With NURBS, the tilt is always smoothly interpolated. However, with Bézier, you can choose the interpolation algorithm between Linear, Ease, B-Spline, and Cardinal, in the .