Steven Padnick let me know about this term, which is not really a comic book term, per se, but more just a literature term that also applies to comic book writing as well as it applies to any other literary medium (Stephen actually used the alternate term, "hang a lantern").
It refers to the practice in stories of addressing reader's questions about the story yourself IN the story. Like if the reader is thinking, "Why didn't they just do ____?," have a character say why they didn't do ____. Or if a reader is thinking, "Boy, that is implausible," have the character remark, "Man, if I didn't see that for myself, I doubt I'd believe it actually happened!" Or if a reader is thinking, "This is just like that one time on ____," have a character remark, "Wow, this is just like that one time on _____." Essentially, address the person's "arguments" before they make them.
Probably the most notable example of hanging a lampshade is when characters acknowledge that what is happening to them seems like something that would happen in a TV show/movie/comic, and that's where the story is actually happening.
It differs in my mind from a "Cousin Larry trick" because hanging a lampshade is an intentional admittance of reader concerns, while a Cousin Larry trick is an after-the-fact attempt to deflect legitimate concern.