Metaphor 

Representation (even better a Transportation/Transfer of meaning)

The actual meaning of the word metaphor is from the Greek meta (μετά) - meaning after, beyond and over, and fora (φορά) - meaning direction and carrying, thus it really means a change in direction, a transportation, a moving from one place to another. In modern Greek metaphora (μεταφορά)  still means exactly that: transportation. It is a transportation of meaning from one word to another.

Definition: The meaning of a word expands and moves by analogy to other words that happen to have some small or great resemblance with the first, which replaces them and makes new (sometimes extraordinary in their conception) expressions.

Examples: 

• Biblical:

• The Lord is my Spepherd- Psalm 23:1

• All flesh is grass - Isaiah 40:3
• Ye are the salt of the earth - Mathew 5:13
• I am the bread of life - John 6:35
  

• Classical:
  

• He weaved his new malice - Homer
• God lit the light of mind in the soul - Aristotle

• Modern:
  

• With the first drop of rain the summer was killed - Elytis
• Love drained in leaky souls - Seferis
• the ship plows the sea. -Abbott & Seeley
• All the world's a stage.-Shak
• “My Life had stood – a Loaded Gun - / In corners – till a Day / The Owner passed – identified - / And carried me away” - Dickinson
• The metling watches painting, by Salvador  Dali, to imply that time passes quickly 

To make it more clear, it is declaration that one thing is, or resembles another. It is sometimes confused with Simile which resembles it and Hypocatastasis which implies it.

[An example, in order to understand the difference would be with the word "pig" when used with food:

• Simile = you eat like a pig 
• Metaphor  = you are a pig
  
• Hypocatastasis = pig!

I hope you do get the point...]