The laryngeal nerve runs from the brainstem (it's a branch of the vagus or tenth cranial nerve) to the larynx (voicebox). It's a nerve that evolved early in the vertebrate line appearing in fish where it ran from the brain, past the heart, directly to the gills. With tetrapod evolution, the neck extended and the heart moved lower into the thorax. Natural selection resulted in the nerve gradually lengthening with these changes such that, in modern mammals, the nerve runs from the brain, down around the heart, and then back up to the voicebox. A totally circuitous route.
Biologists, like retired Oxford professor and evolutionary biologist Richard Dawkins above, have argued that the recurrent laryngeal nerve is a kludge and direct evidence against the religiously-motivated idea of intelligent design. Neil Shubin also makes this argument in his wonderful book Your Inner Fish.
There are a number of anatomical features like this that make absolutely no sense from a design standpoint but are perfectly understandable in an evolutionary context.