In Cognitive linguistics, metonymy is one of the basic characteristics of Cognition. It is extremely common for people to take one well-understood or easy-to-perceive aspect of something and use that aspect to stand either for the thing as a whole or for some other aspect or part of it.
In Rhetoric, metonymy is the substitution of one word for another with which it is associated.
In linguistics, as in rhetoric, the distinction between metaphor and metonymy is important. Two examples using the term "fishing" help make the distinction clear (example drawn from Dirven, 1996).
The phrase "to fish pearls" uses metonymy, drawing from "fishing" the idea of taking things from the ocean. What is carried across from "fishing fish" to "fishing pearls" is the domain of usage and the associations with the ocean and boats, but we understand the phrase in spite of rather than because of the literal meaning of fishing: we know you do not use a fishing rod or net to get pearls.
In contrast, the metaphorical phrase "fishing for information", transfers the concept of fishing (waiting, hoping to catch something that you can't see) into a new domain.
Thus, metonymy works by calling up a domain of usage and an array of associations (in the example above, boats, the ocean, gathering life from the sea) whereas metaphor picks a target set of meanings and transfers them to a new domain of usage.
They gradually ascended for half-a-mile, and then found themselves at the top of a considerable eminence, where the wood ceased, and the eye was instantly caught by Pemberley House, situated on the opposite side of a valley, into which the road with some abruptness wound. It was a large, handsome stone building, standing well on rising ground, and backed by a ridge of high woody hills; and in front, a stream of some natural importance was swelled into greater, but without any artificial appearance. Its banks were neither formal nor falsely adorned. Elizabeth was delighted. She had never seen a place for which nature had done more, or where natural beauty had been so little counteracted by an awkward taste. Jane Austen, Pride and Prejudice, Chapter 43.
Austen describes the house and Elizabeth's admiration for the estate at length as an indirect way of describing her feelings for Mr. Darcy himself. One could attempt to read this as an extended metaphor, but such a reading would break down as one tried to find a way to map the elements of her description (rising ground, swollen river) directly to attributes of her suitor. Furthermore, an extended metaphor typically highlights the authors ingenuity by maintaining an unlikely similarity to an unusual degree of detail. In this description, on the other hand, although there are many elements of the description that we could transfer directly from the grounds to the suitor (natural beauty, lack of artifice), Austen is emphasizing the consistency of the domain of usage rather than stretching to make a fresh comparison: each of the things she describes she associates with Darcy, and the end we feel that Darcy is as beautiful as the place to which he is compared and that he belongs within it. Metonymy of this kind thus helps define a person or thing through a set of mutually reinforcing associations rather than through a comparison.
Advertising frequently uses this kind of metonymy, putting a product in close proximity to something desirable in order to make an indirect association that would seem crass if made with a direct comparison.
When the distinction is made, it is the following: if A is used to refer to B, it is a synecdoche if A is a part of B and a metonymy if A is commonly associated with B but not a part of it.
Thus, "The White House said" would be a metonymy for the president and his staff, because the White House (A) is not part of the president or his staff (B), it is merely closely associated with them because of physical proximity. On the other hand, asking for "All hands on deck" is a synecdoche because hands (A) are actually a part of the men (B) to whom they refer.
There is a famous example which displays synecdoche, metaphor and metonymy in one sentence. "Fifty keels ploughed the deep", where "keels" is the synecdoche as it takes a part (of the ship) as the whole (of the ship), but keels are not an inherent quality of 'shipness'; "ploughed" is the metaphor as it substitutes (thus also displacing it) by association the concept of sailing; and "the deep" is the metonym, as "deepness" is an inherent quality or attribute of seas and oceans and directly affects their defintition.