What is the difference of the words "supple" and "flexible" and specially where are they preferred to the other?
When I looked up supple in NOAD, it said, "See note at flexible." Here is that note:
THE RIGHT WORD
If you can bend over and touch your toes, you are flexible.
But a dancer or gymnast is limber, an adjective that specifically applies to a body that has been brought into condition through training (: to stay limber, she did yoga every day).
Flexible applies to whatever can be bent without breaking, whether or not it returns to its original shape (: a flexible plastic hose; a flexible electrical conduit); it does not necessarily refer, as limber does, to the human body.
Unlike flexible, resilient implies the ability to spring back into shape after being bent or compressed, or to recover one's health or spirits quickly (: so young and resilient that she was back at work in a week).
Elastic is usually applied to substances or materials that are easy to stretch or expand and that quickly recover their shape or size (: pants with an elastic waist), while supple is applied to whatever is easily bent, twisted, or folded without breaking or cracking (: a soft, supple leather). When applied to the human body, supple suggests the ability to move effortlessly.
Pliant and pliable may be used to describe either people or things that are easily bent or manipulated. Pliant suggests a tendency to bend without force or pressure from the outside, while pliable suggests the use of force or submission to another's will. A pliant person is merely adaptable, but a pliable person is easy to influence and eager to please.
There may be some exceptions, but, as a general rule, supple applies more to skin, fabrics, and materials.
In other words, a flexible hose would be easy to bend or coil, while a supple hose would be easy to pinch or crimp.
adjective ( -pler, -plest)
bending and moving easily and gracefully; flexible : her supple fingers | figurative my mind is becoming more supple. See note at flexible .
• not stiff or hard; easily manipulated : this body oil leaves your skin feeling deliciously supple.
capable of bending easily without breaking : flexible rubber seals.
• able to be easily modified to respond to altered circumstances or conditions : flexible forms of retirement.
• (of a person) ready and able to change so as to adapt to different circumstances : you can save money if you're flexible about where your room is located.
Basically, when referring to movement, if something is 'supple' it means it moves easily, and is thus flexible.
Using the example of a branch and a arm.
A branch would be flexible because you can bend it before it breaks, but it is not supple because when you touch it the surface is rough and coarse.
An arm would be flexible because you can bend it before it breaks and it is supple, because when you touch the skin, it's soft and smooth and flexible.