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.

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
 To shed crocodile tears
 To cry about something but without actually caring.
 Wild goose chase
 A useless journey or pursuit.
 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.
 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.
 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

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.

References 

Figures of speech