A groan-inducing pun would be a play on words that causes one to
respond with a groan. The reasons for groaning in response to a pun
may vary, but in general it would be a way of acknowledging a
particularly bad, lame, or cheesy pun. A groan could also be a way
of appreciating a clever pun without breaking a perceived social
barrier for laughing at puns. Lastly, a groan could be caused by a
mixed emotional response of irritation and entertainment or an
expression of jealousy that the groaner did not think of the pun
first. In most cases, however, a groan-inducing pun would be an
especially bad one.