Latin for "(it) does not follow". Applied to a statement that's supposed to be a logical consequent of a line of reasoning but in fact is not. Technically, a non sequitur is a superclass of many logical fallacies for which a putative consequent doesn't follow the precedent, such as Undistributed Middle and Argument By Analogy, but use should be restricted to consequents that don't fall into another class. For example, in the argument: "Socrates is a man and men are mortal, therefore Socrates is dead," the fragment "Socrates is dead" is a non sequitur. The greater the apparent randomness of a supposed consequent, the more likely to be accurate is the appellation.
Often used of Off The Wall remarks in ordinary discourse.
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