It refers to electro-chemical impulses in our brain. When you learn something new your brain creates neurological electro-chemical connections. This is called to wire the brain. Then you need to update your knowledge and adapt to a new situation the brain restructures these connections. This is called rewiring.

Rewiring usually means taking out old wiring e.g. in a house, and replacing it with new wiring probably in a new configuration. So paraphrasing your sentence. New technology is altering our brains to do more things and it is not good for our brains.