Right or left orientation, chirality, appears in many ways.
Asymmetry appears in objects in the universe on every scale-- Subatomic particles, atoms, molecules, living things, planetary systems and galaxies, perhaps the entire universe-- all have chiral, mirror rotational, or, from some perspective, a right or left orientation.
Some molecules come in right-handed and left-handed variations. Amino acids are one example.
Amino acids, which form proteins vital to life, come in left-handed and right-handed versions, with the exception of the simplest one, glycine, which happens to be symmetrical. Living things mostly use the left-handed amino acids. Examples of L-amino acids include L-Lysine, L-Glutamine and L-Serine. Animal proteins usually contain the L-version. The D-version (right handed) is seldom used. The "L" and "D" prefixes come from Latin, laevus (left) and dexter (right), which is the root of dexterity and dexterous.
Animal structures and organs are frequently left or right oriented.
Most spiral sea shells, and snails, viewed from the top, tend to spiral to the right. Some may spiral left. Sea shells tend to spiral the same way within any species. Perhaps they get along better that way.
Fiddler crabs have a large claw, one side or the other.
The chiral placement of mammal organs is usually fairly regular. Sperm whales most often have a blowhole slightly to the left. A man's penis usually hangs slightly to the left. Mammal hearts are normally on the left side. The stomach and bowels usually orient and rotate in the same direction.
"How does that happen?", might be dismissed as "it's in the genes", but, why does it happen? seems to be a mystery.
Most people are right handed; some left handed; a few are considered ambidextrous.
Some famous boxers, baseball batters and pitchers, tennis players, and sword fighters, were born "lefties", and used that difference to their advantage.
Some have linked right and left handedness to the way a person's hair whorls around, but this idea has been questioned. Parting of the hair tends to correspond to the whorl, and may relate to a person's handedness.
At the wedding altar a man will usually be seen to the left of the woman when facing the congregation, but, turned to face the minister, the man is usually to right of the woman. It's the same in bed. A man will tend to lay on the right hand side of a woman. A right-handed reach is easier from that side.
When you meet someone for the first time, you might notice where they part their hair. Part on left, part on right, there's a good guess about whether they are right-handed or left-handed, respectively. Parted close to, or on, the middle, maybe ambidextrous, and could prefer one hand or the other, depending on circumstances. Of course it helps to notice their hands, which hand gestures more, which uses a screwdriver, which throws a ball, uses a hammer, and so on.
There are some rare cases where the normal turn of events doesn't happen. There are rare anatomical configurations. In cases of dextrocardia situs inversus, the heart is on the right side of the chest. With dextrocardia situs inversus totalis, most or all organs are switched right for left. This sometimes, rarely, happens with one of genetic twins.
No one knows why some scenarios are left-handed and some are right-handed; the reasons for chirality in the universe are a mystery.
Someone here mentioned this recent video regarding snail shell handedness.
Snakes spare anti-clockwise snails.
I can't help mentioning my laughter at the part about anti-clockwise snails surviving longer, but having trouble mating with the clockwise ones.