Idiom

An idiom is a common phrase which means something different from its literal meaning but can be understood because of their popular use.
Idioms are difficult for someone not good at speaking the language. Some idioms are only used by some groups of people or at certain times. The idiom shape up or ship out, which is like saying improve your behavior or leave if you don't, might be said by an employer or supervisor to an employee, but not to other people.
Idioms are not the same thing as slang. Idioms are made of normal words that have a special meaning known to almost everyone. Slang is usually special words, or special meanings of normal words that are known only to a particular group of people.
To learn a language a person needs to learn the words in that language, and how and when to use them. But people also need to learn idioms separately because certain words together or at certain times can have different meanings. In order to understand an idiom, one sometimes needs to know the culture from which the idiom comes.
To know the history of an idiom can be useful and interesting. For example, most native British English speakers know that "No room to swing a cat" means "there was not much space" and can use the idiom properly. However, few know this is because 200 years ago sailors were punished by being whipped with a "cat o' nine tails". A big space was cleared on the ship so that the person doing the whipping had room to swing the cat.
An idiom is a phrase whose meaning cannot be understood from the dictionary definitions of each word taken separately. The linguist's term for the real meaning of an idiom is the subtext.
Simple Definition
Idioms are phrases or expressions that have a figurative meaning different from their literal interpretation. They are commonly used in everyday language to convey a specific idea, often with cultural or historical significance. Idioms are not meant to be taken literally, and their meaning can be understood only by familiarizing oneself with their usage and context.
Some common idioms
Break a leg
A way to wish someone good luck.
To live it up
To enjoy life, to live widely
To kick the bucket
To die.
Shape up or ship out
Used to tell someone that they should leave if they don't improve their behavior or performance
Learn the ropes
Learn and often perfect the skills of a craft, job, etc.
Mad as a hatter
Mentally unstable, especially as the result of poisoning.
To shed crocodile tears To cry about something but without actually caring.
Wild goose chase A useless journey or pursuit.
Nothing burger An idea or promise without substance
There's no room to swing a cat
There is not a lot of space.
To pay through the nose
To pay a lot of money, more than is normal.
Cost an arm and a leg
Be extremely expensive.
To bark up the wrong tree
To choose the wrong course of action.
To spill the beans
To tell a secret.
It's raining cats and dogs
It's raining heavily.
To get into hot water
To get into trouble.
Skate on thin ice
To disregard caution.
Chicken-hearted
Frightened or cowardly
To chicken out
Not doing a thing, because of fear.
Top dog
Leader.
To smell a rat
To think that something is wrong.
To give up
To quit.
To give up on
To stop believing in something or someone.
I could eat a horse
I am very hungry.
To be on top of the world
To be really happy.
Once in a blue moon
Rarely
Wouldn't touch with a ten-foot pole! (Or barge pole in British English)
Not wanting anything to do with something or someone.
Avoid like the plague
Avoid at any cost.
Miss the boat
Be too late for a chance or opportunity.
Child's play
Easy to do.
Cakewalk
Something easy to accomplish.
Chinese puzzle
Extremely difficult task.
Castle in the clouds or pie in the sky
An impossible or improbable dream, project, etc.
Hit the sack
To go to bed
Get\give the sack
Dismiss or be dismissed from one's employment.
The whole nine yards
Everything
Bells and whistles
All the unnecessary luxuries, features, etc
Mad as a hater
Insane, as from poisoning.
Turn a blind eye \ deaf ear
To ignore.
Cry wolf
Report a false emergency.
One's cup of tea
What someone prefers.
Not for all the tea in China
Less common idioms include
Safe as houses
Very safe and secure.
Idioms which have unclear meaning
Articles by Oxfam and the BBC have said that many idioms in English are unclear, or ambiguous. Many are understood differently in different countries. Many of the examples are taken from face-to-face talk, but may also apply in written reports.
Examples
Satisfactory (in a report, or in an assessment) might mean not satisfactory.
I hear what you say. Might mean I'm listening, but more likely I totally disagree.
With the greatest respect. May mean You are quite wrong. 68% of British thought it meant "I think you are an idiot", whereas 49% of Americans thought it meant "I am listening to you".
I'll bear it in mind. In a survey 55% of British thought it meant I've forgotten it already. 43% of Americans thought it meant I will probably do it.
Vocables are sounds that are not proper words, but mean something, and are often ambiguous. One is a long drawn-out sound hmmmmmm.
One suggestion is that these idioms are used to smooth over difficult areas in social interaction. They cover passive-aggressive statements which might cause more conflict if openly expressed.