Is it a metal?
No. It is thread, each strand thinner than a hair and almost pure carbon, made by slowly baking a plastic fiber until everything else has burned away.
Then what am I holding?
Cloth woven from that thread, set in resin and cured under pressure. The weave you see is real; the gloss is the resin.
Why do bikes and race cars use it?
For its weight it is stiffer than steel and stronger than aluminum, and when every gram counts, few materials come close.
What happens when it is dropped?
Usually nothing. Then one day it cracks through. Metal dents and carries on; carbon fiber shows no marks until it fails, and it cannot be hammered straight or welded.
How does it feel?
Hard, a little cold, and light enough to surprise you the first time you pick it up. It is at its best in things that are handled every day but rarely dropped: a ruler, a pen, a coaster on a desk.