Neural wiring is a term used to describe the structure and function of the brain. A google search for "neural wiring" gave me 830,000 results. I have also heard this term used in personal conversation, and while going to graduate school in education.
Nerves are kind of like wires. They are long and thin, and carry signals through electricity. Nerves are kind of not like wires because they are not metallic, they have much more structure than a simple wire, and they are squishy. Squishy means that instead of just transmitting electrical systems, they also diffuse chemicals. In addition, a neuron has thousands of connections, while most wiring has only a few connections.
So it is an imprecise metaphor. Maybe a helpful metaphor at times. But I have heard it used as a metaphor so many times that I think to many people, it has gone beyond being a metaphor and is taken to be a literal truth out our brain: that our nerves are bundles of tiny little wires.
Which can lead to some interesting thoughts, when you take it literally: in the aforementioned google search results, the first result is a claim by Naomi Wolf that "neural wiring" explains clitoral versus vaginal orgasms. Although a serious complaint could be made about this represents the technologicalization of sexuality, the more immediate and incongruous image is of little plastic coated wires (perhaps with some capacitors or even vacuum tubes running all over someone's genitals, an image that is unappealing unless you have very precise fetishes.
In any case, "neural wiring" is a phrase we are probably going to hear over and over again until our next technological paradigm gives us another incorrect metaphor. In the meantime, try to remember that "neural wiring" is just a metaphor, and not the best one.