When you replace one thing (or idea) with a different thing (or idea) to make a stronger point, you use a metaphor. (Don't compare two things using the words like or as, or you have a simile.)
Metaphors put clear pictures into people's minds, and they make your writing more interesting. Look at these pairs of sentences. Which sentence of each pair puts a clearer picture into your mind?
Examples: metaphors
In each of these pairs of sentences, the second one contains metaphors.
My daughter's angry words hurt me very much. -or-
My daughter's angry words knifed me in the heart. (There are two metaphors here. The knife metaphor represents the emotional pain the words caused. The heart metaphor represents the person's feelings.)
[A person is admiring an great-looking, fast sports car, and says]
Man, this car looks really fast! -or-
Man, this beast is a rocket! (Two more metaphors! The beast metaphor represents the aggressive and powerful look of the car. The rocket metaphor compares the speed of the car to the speed of a rocket.)
[A person finally pays off a large debt, and says:]
I just paid off my credit card! -or-
I just escaped from the jaws of debt. (The person used the idea of jaws to give a stronger picture about what it was like to be in debt.)
Non-Examples
That car is like a rocket! (Because you used the word like, you used a simile, not a metaphor.)
My high rent payment is as painful as a bee sting. (You used a simile (not a metaphor) because you used the word as to compare two different things. If you would have said that your mortgage payment is a bee sting, then you would have used a metaphor.)
Those flowers have soft, dewy petals. (You're not comparing anything, you're just describing. So, you don't have a metaphor. If you would have said that your sleeping daughter's face is an arrangement of rose petals on the pillow, then you would have used a metaphor.)