Say it with us, Shmoopers, ZOOG-muh.
This one's a bit tricky, so we'll lead with some examples:
He was alternately cudgeling his brains and his donkey.
He carried a strobe light and the responsibility for the lives of his men.
Get out of my dreams and into my car. (Billy Ocean)
My teeth and ambitions are bared. Be prepared! (Scar)
Some of those are funny (Dickens sure could land a joke), and some of them are serious, but all of them are zeugmas.
A zeugma uses one word to relate to or control two other words in the sentence, which might not have anything to do with each other. Often folks use this device to humorous effect, because the image of cudgeling brains and a donkey all at once is, when you think about it, pretty hilarious. By putting together two very unlike objects or concepts, zeugmas make us laugh, or at least crack a smile or two.
Plus, the pairing also invites comparison—how are teeth like ambitions? And what does a strobe light carried by a soldier in Vietnam have to do with the lives of the men in his command? Maybe more than you think.