A wish is a hope or desire for something. Fictionally, wishes can be used as plot devices. In folklore, opportunities for "making a wish" or for wishes to "come true" or "be granted" are themes that are sometimes used.
In fiction a wish is a supernatural demand placed on the recipient's unlimited request. When it is the center of a tale, the wish is usually a template for a morality tale, "be careful what you wish for"; it can also be a small part of a tale, in which case it is often used as a plot device. One can wish on many things for example: wishing wells, dandelions when one blows the seeds or light them on fire, stars and much more. When one wishes in a well he or she throws money in, in the hope his or her wish comes true, the money normally goes to a charity.
A template for fictional wishes could be The Book of One Thousand and One Nights, specifically the tale of Aladdin, although in the tale of Aladdin the actual wishes were only part of the tale. Also, Aladdin's demands, while outrageous, were mainly variations on wealth (which is still often taken as the most common request).
Classically the wish provider is often a spirit, genie or similar entity, bound or constrained within a commonplace object (Aladdin's oil lamp for example) or a container closed with Solomon's seal. Releasing the entity from its constraint, usually by some simple action, allows the object's possessor to make a wish.
The subservience of the extraordinarily powerful entity to the wisher can be explained in several ways. The entity may be grateful to be free of its constraint and the wish is a thank-you gift. The entity may be bound to obedience by its prison or some other item that the wisher possesses. The entity may, by its nature, be unable to exercise its powers without an initiator.
Other wish providers are a wide variety of, more or less, inanimate objects. W.W. Jacob's Monkey's Paw is an example of this. Piers Anthony puts a spin on this idea in Castle Roogna: a magic ring claims to grant wishes and then claims credit when a wish comes true, apparently from the unaided efforts of the characters—but every wish made on the ring sooner or later comes true.