In Latin, non sequitur means "it does not follow." The phrase was borrowed into English in the 1500s by people who made a formal study of logic. For them it meant a conclusion that does not follow from the statements that lead to it.
What is the meaning of sequiturs?
: the conclusion of an inference : consequence.
Why do people use non sequiturs?
In literature, non sequiturs are often used for comedic purposes, as in the Theater of the Absurd. In these instances, something is stated that bears no relevance to what was being discussed. These non sequiturs are so far-fetched, they serve as a literary technique for some added texture and comedy.