These are extra settings for Hair Particles used by Cycles.
There are also scene level hair settings which can be found with the Geometry settings.
The Cycles Hair Settings, under the particle tab, are used to control each hair particle system's strand properties.
A shape parameter that controls the transition in thickness between the root and tip. Negative values make the primitive rounded more towards the top, the value of zero makes the primitive linear, and positive values make the primitive rounded more towards the bottom.
Multiplier of the hair width at the root.
Multiplier of the hair width at the tip.
Multiplier for the Root and Tip values. This can be used to change the thickness of the hair.
Sets the thickness at the tip to zero, even when using a non-zero tip multiplier.