
Carbon in the form of graphite is soft, slippery and easily broken. But very thin filaments of carbon are very stiff. These carbon fibres are useful for reinforcing other materials to make them tougher. They are embedded in strong plastics to make composite materials. These are usually very strong but lightweight, so they are used for skateboards, boat hulls and high performance sports equipment.
You may wish to view this BBC News item from 2006 about a £7000 mountain bike, made from carbon fibres and titanium, that weighs just 6 kg.
Kevlar® is a very strong artificial fibre. It is woven to make a material that is used for light and flexible body armour. It is strong and tough because:

A section of a Kevlar® molecule