Amplifying Isuzurover's explanation. A conventional spring has the spring leaves of the same thickness throughout their length, with the taper needed* on the spring provided by different lengths on each leaf. The leaves rub on each other the whole length of contact, and provide frictional damping, so they are only partly dependent on the shock absorbers for damping.

"Parabolic" springs have only two or three leaves, with all leaves usually full length, and the necessary taper provided by tapering the thickness of each leaf according to a parabolic function. The leaves are thicker at the axle, and arranged so that they only touch at the tips, often via a nylon slipper, and friction is minimal. This gives very little frictional damping, so that ride is better for small bumps, but more damping from the shock absorbers is required, hence special shock absorbers are needed.

Parabolic springs should, in theory, provide a better ride than conventional springs, although the difference is insignificant for well oiled conventional springs. However, when parabolics are fitted, it is usually to replace springs that are in very bad condition, and unsurprisingly, the improvement in ride is very evident.

The only real disadvantage of the parabolic springs is that since the strain on the leaves is greater than for the normal spring leaves (the same deflection for a thicker leaf means greater strain on the material), to achieve the same resistance to failure calls for better quality metallurgy and surface finish, and it is not always clear that this is happening.

*For a spring such as the semi-elliptic ones on Landrovers, the bending moment on the spring is greatest at the axle, and decreases towards each end. To spread the bending equally along the length of the spring, the resistance to bending has to taper in the same way that the bending moment does.

John