MacGuffin (a.k.a. McGuffin or maguffin) is a term for a motivating element in a story that is used to drive the plot. It actually serves no further purpose. It won't pop up again later, it won't explain the ending, it won't actually do anything except possibly distract you while you try to figure out its significance. In some cases, it won't even be shown. It is usually a mysterious package/artifact/superweapon that everyone in the story is chasing.
To determine if a thing is a MacGuffin, check to see if it is interchangeable. For example, in a caper story the MacGuffin could be either the Mona Lisa or the Hope diamond, it makes no difference which. The rest of the story (i.e. it being stolen) would be exactly the same. It doesn't matter which it is, it is only necessary for the characters to want it.
A common MacGuffin story setup can be summarized as "Quickly! We must find X before they do!".
The term was popularised by Alfred Hitchcock, who actually credited one of his screenwriters, Angus McPhail, with the creation of this concept and the name for it, citing a particular school-boy joke:
A man is riding on a train when a second gentleman gets on and sits down across from him. The first man notices the second is holding an oddly shaped package.
"What is that?" the first man asks.
"A MacGuffin, a tool used to hunt lions in the Scottish highlands."
"But there are no lions in the Scottish highlands," says the first man.
"Well then," says the other, "That's no MacGuffin".
Hitchcock and Angus McPhail were not the first to formulate this concept. Silent-film actress Pearl White starred in cliffhanger serials (most famously "The Perils of Pauline") in which the characters spent most of their screen time chasing each other for possession of a roll of film, or some other doodad. This device occurred so often in Pearl White's serial films that she routinely referred to the coveted object as a "weenie", using the term precisely as Hitchcock would later use "MacGuffin".
In academic circles this is sometimes called the Golden Fleece, after the artifact from the myth of Jason and the Argonauts. The Fleece was first mentioned by the Greek poet Simonides, which makes this trope Older Than Feudalism.
Compare Magnetic Plot Device. Contrast Mock Guffin, for when an object that isn't really a MacGuffin is mistaken for one. If it's more than just a something to keep the plot moving, it's probably a Chekhov's Gun. (Though that only counts if it's initially introduced as being unimportant.)
If you want to start arguing that your favourite series most awesome magical thing isn't a MacGuffin, remember that Tropes Are Tools. Having a MacGuffin is not necessarily Bad Writing, depending on how it's handled. Sometimes, it can even enhance the work!