A metaphor is a literary figure of speech that describes a subject by asserting that it is, on some point of comparison, the same as another otherwise unrelated object. Metaphor is a type of analogy and is closely related to other rhetorical figures of speech that achieve their effects via association, comparison or resemblance including allegory, hyperbole, and simile.
One of the most prominent examples of a metaphor in English literature is the All the world's a stage monologue from As You Like It:
All the world?s a stage, And all the men and women merely players; They have their exits and their entrances;
William Shakespeare, As You Like It, 2/7
This quote is a metaphor because the world is not literally a stage. By figuratively asserting that the world is a stage, Shakespeare uses the points of comparison between the world and a stage to convey an understanding about the mechanics of the world and the lives of the people within it.