Strange cures create a stimulus that interrupts the reflex.
Several bodily functions can be played for laughs, and hiccups are one of them. Hiccups are usually minor and short-lived, if a little embarrassing and inconvenient. But they're often associated with good times — a bit of overeating, perhaps, or getting tipsy. The sound itself is funny.
Some of the remedies are amusing, too: drinking from the wrong side of the glass, having someone jump out at you and shout "boo," biting a lemon, and drinking pickle juice, to name a few. "It is good to cast colde water in the face of him that hath the hicket," was the advice in 16th-century England. There are also standbys like holding your breath or breathing into a paper bag. Some of these cures make more sense than others, but they're all pretty much untested.