For the most part, everything we say falls under two linguistic categories: literal language and figurative language. In literal language, what we say is exactly what we mean. In figurative language (also known as "figures of speech"), what we say does not necessarily equal what we mean.
Let's start with a rather simple example: Paris Hilton turned this expression into a trite, overused cliché (which she also tried to patent): that's hot. 
On the one hand, a person may take this expression and interpret it as displayed on the greeting card: something feels warm to the touch, or hot.
On the other hand, we can estimate 99.9% of the time Paris said that's hot, she didn't mean warm to the touch. She meant nifty or sexy. But even those words have double-meanings as well.
So how do we know that what someone says is or isn't what he means? Sometimes we can take into account the person's tone of voice or the context. Often, poetry contains much figurative language. This makes stories or poetry more interesting to read. Here are some examples of different types of figurative language:
antithesis: an opposition, or contrast, of ideas example: "It was the best of times, it was the worst of times..." ~ Charles Dickens, A Tale of Two Cities
euphemism: a device in which indirectness replaces directness of statement, usually in an effort to avoid offensiveness use of 'correctional facility' in place of 'prison'
hyperbole: a figure of speech that uses an incredible exaggeration, or overstatement, for effect example: "People moved slowly then. There was no hurry, for there was nowhere to go, nothing to buy and no money to buy it with, nothing to see outside the boundaries of Maycomb County." ~ Harper Lee, To Kill a Mockingbird
metaphor: a figure of speech that makes a comparison between two unlike things without the use of such specific words of comparison as like, as, than, or resembles example: Emily Dickinson, "Fame is a Fickle Food"
extended metaphor: an extended metaphor, or conceit, sets up a principal subject with several subsidiary subjects or comparisons credit example: "All the world's a stage / and all the men and women merely players / they have their exits and entrances" ~ William Shakespeare, As YouLike It
metonymy: the substitution of the name of an object closely associated with a word for the word itself example: "The body that controlled the crown was, it is true, a narrow one." ~ T. F. Tout, The History of England
oxymoron: a combination of contradictory terms example: "I will complain, yet praise" ~ George Herbert, "Bitter-Sweet"
paradox: a statement that seems contrary to common sense yet may, in fact, be true example: Hamlet to his Uncle Cladius: "A little more than kin, and less than kind." (Hamlet's first words in the play show him playing with words in order to state a paradox: Claudius is twice related to him, as uncle and stepfather, but not really his kin or kind at all.) ~ William Shakespeare, Hamlet
personification: a figure that endows animals, ideas, abstractions, and inanimate objects with human form; the representing of imaginary creatures or things as having human personalities, intelligence, and emotions example: Cheshire Cat in Alice in Wonderland
simile: a figure of speech that makes an explicit comparison between two unlike things, using a word such as like, as, than, or resembles example: "When the companies were thus arrayed, each under its own captain, the Trojans advanced as a flight of wild fowl or cranes that scream overhead when rain and winter drive them over the flowing waters of Oceanus to bring death and destruction on the Pygmies, and they wrangle in the air as they fly" ~ Iliad of Homer
synecdoche: a part signifies the whole or the whole signifies the part; a good synecdoche out to be based on an important part of the whole, and, usually, the part standing for the whole ought to be directly associated with the subject under discussion example: " 'Johansen,' Wolf Larsen said briskly to the new mate, 'keep all hands on deck now they're here. Get in the topsails and outer jibs. We're in for a sou'easter. Reef the jib and the mainsail, too, while you're about it.' " (all hands on deck = all the help available) ~ Jack London, The Sea Wolf
understatement: stating an idea with restraint (holding back) to emphasize what is being talked about example: "we carried them home and put them in Aunt Patsy's work basket for a surprise; for she was prejudiced against snakes, and always when she took the basket in her lap and they began to climb out of it it disordered her mind" ~ from Mark Twain's autobiography
symbol: a person, place, thing, or event that has meaning in itself and that also stands for something more than itself example: the conch shell as a symbol of civilization and order in Lord of the Flies
verbal irony: occurs when someone says one thing but really means something else example: "Come," I said, are rich, respected, admired, beloved; you are happy, as once I was. You are a man to be missed. For me it is no matter. We will go back; you will be ill, and I cannot be responsible. Besides, there is Luchresi --" ~ Edgar Allan Poe, "The Cask of Amontillado"
Indiana Academic Standard for English / Language Arts
10.1.2: Literal and figurative meanings
For more information, consult your literature textbook or visit Wikipedia's article on literal and figurative language here.