1. A statement that does not follow logically from what preceded it: "Someone once said that Napoleon Bonaparte was a short man. A student who was making a report in history class included a non sequitur that stated that because Napoleon was so short and ego centric, he never allowed any of his officers to be any taller than he was."
2. A statement containing an illogical conclusion.
3. In logic, a conclusion that does not follow from the premises.

A non sequitur is a literary device; in comedy, it is a comment which, due to its lack of meaning relative to the comment it follows, is absurd to the point of being humorous. Its use can be deliberate or unintentional. Literally, it is Latin for "it does not follow".

In other literature, a non sequitur can denote an abrupt, illogical, unexpected, or absurd turn of plot or dialogue not normally associated with or appropriate to that which preceded it.

It does not follow.

In formal logic a non sequitur is a faulty conclusion arrived at by violating a principle of sound reasoning.

A common example is false generalization. In the sentence pair "It was that California guy who hotwired my car so he could steal it" and "All of these Californians are dirty thieves," the second sentence doesn't logically follow from the first; so, it is a non sequitur.

Logical fallacy: non sequitur quotes.