A parody is a text that imitates another work or genre for the sake of a good, hearty laugh. Don't confuse this with satire, which also gets a laugh but isn't in it just for the chuckles. Parodies aren't meant to incite some major social change, and they're not even meant to knock the original work down a notch. We swear—it's really all about the giggles.
Parody has been around for a long time. Heck, Aristotle (that guy who lived in the 4th century BCE and wrote a commentary on pretty much everything) already had something to say about it.
Let's throw some examples your way. Gulliver's Travels is a parody of popular travel narratives. Hey, no offense to popular travel narratives, but they're pretty easy to manipulate into a laugh. "But wait!" you say, "Gulliver's Travels is a travel narrative!" To that we say, "enough with the exclamation points." That's the fun thing about parodies—they take on the form of exactly what they're mocking.
Same goes for Virginia Woolf's Orlando, which is a parody of a biography (in biography form, by definition). The joke at the heart of Orlando is Woolf's use of "biography" (which is all about narrating events in a person's life) to describe what is not eventful (i.e., sensory experience).
Christopher Guest and Greg Daniels have given us modern thinkers an easy way to remember all this: they actually call their parodies "mockumentaries." So if you're having trouble remembering what a parody is, just think about This is Spinal Tap, and everything will be okay. That's a good rule to live by just generally, too.