Less commonly known as Varronian (after Varro) satire, this is a type of satire characterized by a rambling, "formless" form. I think the best example is Rabelais' Gargantua and Pantagruel, or, in English, Swift's Gulliver's Travels. They contain many of the common elements found in Menippean satire: weird locations, a lot of odd rambling and digression, strange characters. Incongruity is the name of the game here: a Menippean satire might be tragic and comic, moralistic and pornographic, it might mix high and low registers, it might mix prose, verse, and drama, all one after the other.
A Menippean Satire is an intellectual satire, usually aimed at people who are stupid, ignorant, bigoted, or close-minded. People who can only think about their jobs, people who think they're "better" than they are, etc, are all ripe targets.
Varro (116 BC - 27 BC) seems to have coined the term in his Saturae Menippeae, after the Greek satirist and Cynic Menippus of Gadara (circa. 290 BC) , but it only came into common use in the 16th century. Like the distinction between "philosophy" and "literature" that Plato and co. came up with, and the more recent term "novel", it has since been projected backwards to cover more ancient texts. Apart from the works of Varro and Menippus themselves, the best known example from ancient times is Petronius' Satyricon, and Seneca's Apocolocyntosis.
Some other examples of this genre are Laurence Sterne's Tristram Shandy, Robert Burton's Anatomy of Melancholy, and, as the helpful softlinker points out, Voltaire's Candide.
Theorist Mikhail Bakhtin is known for his preference of polyvocal dialogy over monology: The existence of several different voices or evaluative accents within a single text. He saw the novel as being the best example of this, with Menippean Satire a close second. Northrop Frye is another recent thinker with concern for this genre (or non-genre, as he would have it).