what is a pun?
The humorous use of a word to emphasize or suggest its different meanings.
It's raining cats and dogs outside. Be careful you don't step in a poodle.
In this example, the pun is that the word puddle is replaced by the word "poodle" to fit with the imagery of the phrase "raining cats and dogs" in the previous sentence. A pun is something that might make you smile but might not make you laugh.
In this example, the pun comes from the tallness of the creature. The phrase a "tall story" is well known as a euphemism to describe a lie. In this case, the giraffe is tall and the phrase "tall story" are combined to tell the reader that the initial question was a lie, thereby creating a joke and a pun at the same time. It's funny but it might make you groan more than laugh.