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 serves no further purpose. It won't pop up again later, it won't explain the ending, it won't 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.
If it passes both of these criteria, congratulations: its a MacGuffin!
A common MacGuffin story setup can be summarized as "Quickly! We must find X before they do!".
The term was popularized by Alfred Hitchcock, who 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.
Contrast Mock Guffin, for when an object that isn't really a MacGuffin is mistaken for one.
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 — concretely defining or giving a central role to the object of a chase can detract from a work, if the point is to focus on the characters.
In The Prayer Warriors, during "The Battle With the Witches", the heroes look for five keys to get into Dumbledore's office in Hogwarts. One is carried by Ginny, another by Ron, a third by Harry, and a fourth by Hermione. It's unclear who has the fifth key, since after the fourth key, the Prayer Warriors break into Dumbledore's office and kill him.
In Catherine and Her Fate, the skein of silk that Catherine's Fate gives her is so apparently worthless that she nearly throws it out. It has, it turns out, two properties: it is exactly the color needed to sew the king's wedding garments, inspiring him to say that she shall have its weight in gold, and it outweighs his entire treasury, thereby inspiring him to demand her story.
The Paranoia adventure "The Yellow Clearance Black Box Blues". The title Black Box. What it does is eventually revealed, in some versions of the adventure, but it's unlikely your player characters will live long enough to discover it.
The "Honor & Intrigue" system has a character attribute actually called "MacGuffin". Taking it turns one of the items in your character's possession into a future MacGuffin.
Referenced in Mistborn Adventure Game, where the book uses the term "MacGuffin" to describe a Secret that has no function other than to be the thing everyone wants. For example, a vast hoard of precious metal that may or may not exist, and which is of little use anyway, because the world is coming to an end and there's nothing to buy with that wealth.
In Philoctetes, while much is made of Philoctetes' special bow (received from Herakles himself) the plot itself is not really concerned with its purpose as much as the choices the characters make because of and in spite of its importance.
In Sherlock Holmes, the MacGuffin is a packet containing letters, photographs, jewelry etc. that were sent to Alice Faulkner's late sister by a foreign gentleman who seduced and ruined her, and the villains want it out of the picture now that he wants to marry. The name of the gentleman is merely whispered inaudibly, and the sister's name is not revealed either.
The Tower of Pimps, a stack of four gold blocks on an obsidian block pedestal, in Rooster Teeth's, "Let's PlayMinecraft". Nothing fancy, just bragging rights material for whoever wins the challenge of the episode.