Literal and figurative language is a distinction within some fields of language analysis. Literal language refers to words that do not deviate from their defined meaning. Non-literal or figurative language refers to words, and groups of words, that exaggerate or alter the usual meanings of the component words.
A literal usage is the "normal" meanings of the words. It maintains a consistent meaning regardless of the context, with "the intended meaning corresponding exactly to the meaning" of the individual words. Figurative use of language is the use of words or phrases in a manner where the literal meaning of the words is not true or does not make sense, but "implies a non-literal meaning which does make sense or that could be true".
Aristotle and later the Roman Quintilian were among the early analysts of rhetoric who expounded on the differences between literal and figurative language.
In 1769, Frances Brooke's novel The History of Emily Montague was used in the earliest Oxford English Dictionary citation for the figurative sense of "literally"; the sentence from the novel used was, "He is a fortunate man to be introduced to such a party of fine women at his arrival; it is literally to feed among the lilies."  This citation was also used in the OED's 2011 revision. 
Within literary analysis, such terms are still used; but within the fields of cognition and linguistics, the basis for identifying such a distinction is no longer used.
Figurative language can take multiple forms such as simile or metaphor.Merriam-Webster's Encyclopedia Of Literature says that figurative language can be classified in five categories: resemblance or relationship, emphasis or understatement, figures of sound, verbal games, and errors.
A simile is a comparison of two things, indicated by some connective, usually "like", "as", "than", or a verb such as "resembles" to show how they are similar.
Example: "His cheeks were like roses, his nose like a cherry.../And the beard on his chin was as white as the snow." (emph added)—Clement Clark Moore
A metaphor is figure of speech in which two "essentially unlike things" are shown to have a type of resemblance or create a new image. The similarities between the objects being compared may be implied rather than directly stated.
Example: “Bark! Bark!” went the dog as he chased the car that vroomed past.
Personification is the attribution of a personal nature or character to inanimate objects or abstract notions, especially as a rhetorical figure.
Example: "Because I could not stop for Death,/He kindly stopped for me;/The carriage held but just ourselves/And Immortality."—Emily Dickinson. Dickinson portrays death as a carriage driver.
An oxymoron is a figure of speech in which a pair of opposite or contradictory terms is used together for emphasis. 
Examples: Organized chaos, Same difference, Military Intelligence
A paradox is a statement or proposition which is self-contradictory, unreasonable, or illogical.
Example: This statement is a lie.
Hyperbole is a figure of speech which uses an extravagant or exaggerated statement to express strong feelings.
Example: They had been walking so long that John thought he might drink the entire lake when they came upon it.
Allusion is a reference to a famous character or event.
Example: Like Hercules, he is so strong.
An idiom is an expression that has a figurative meaning unrelated to the literal meaning of the phrase.
Example: You should keep your eye out for him.
To keep an eye out for someone means to watch out for it.
A pun is an expression intended for a humorous or rhetorical effect by exploiting different meanings of words.
Example: I wondered why the ball was getting bigger. Then it hit me.
"Then it hit me." has two different meanings
Standard pragmatic model of comprehension
Prior to the 1980s, the "standard pragmatic" model of comprehension was widely believed. In that model, it was thought the recipient would first attempt to comprehend the meaning as if literal, but when an appropriate literal inference could not be made, the recipient would shift to look for a figurative interpretation that would allow comprehension. Since then, research has cast doubt on the model. In tests, figurative language was found to be comprehended at the same speed as literal language; and so premise that the recipient was first attempting to process a literal meaning and discarding it before attempting to process a figurative meaning appears to be a false premise.
Reddy and contemporary views
Beginning with the work of Michael Reddy in his 1979 work "The Conduit Metaphor", many linguists now reject that there is a valid way to distinguish between a "literal" and "figurative" mode of language.
^Origin: 1570–80; < Late Latin < Greek onomatopoiía making of words = onomato- (combining form of ónoma name) + poi- (stem of poieîn to make; see poet) + -ia -ia"Onomatopoeia". onomatopoeia, n. Oxford English Dictionary.
^Origin: 1745–55; personi(fy) + -fication"Personification". personification, n. Oxford English Dictionary.
^Origin: < post-classical Latin oxymoronfigure of speech in which a pair of opposed or markedly contradictory terms are placed in conjunction for emphasis (5th cent.; also oxymorum) < ancient Greek ὀξυ-oxy- comb. form1+ μωρόςdull, stupid, foolish (see moron n.2)."Oxymoron". oxymoron. Oxford English Dictionary.
^Origin: < Middle French, French paradoxe(1495 as noun; 1372–4 in plural paradoxesas the title of a work by Cicero; paradoxon(noun) philosophical paradox in post-classical Latin also a figure of speech < ancient Greek παράδοξον, especially in plural παράδοξαStoical paradoxes, use as noun of neuter singular of παράδοξος(adjective) contrary to received opinion or expectation < παρα-para- prefix1+ δόξαopinion (see doxology n.), after ancient Greek παρὰ δόξανcontrary to expectation"Paradox". paradox, n. Oxford English Dictionary.
^Origin: < Greek ὑπερβολήexcess (compare hyperbola n.), exaggeration; the latter sense is first found in Isocrates and Aristotle. Compare French hyperbole(earlier yperbole)."Hyperbole". hyperbol e, n. Oxford English Dictionary.