Sometimes a person will tell a story which is untrue, with the purpose of bringing levity to a conversation. This may be termed a joke. These stories may also be used to illustrate a point.
It's important to note that such cases are not always clearly signaled as being humor or untrue. It is a part of the joke's effect that the reader or listener will not at first know it is a joke, but will realize it after noticing an absurdity.
A related concept is "dry humor".