There are many effects of stress on the brain, so I will focus on just a couple of examples of stress and brain function.
In normal functioning, the body would send glucose to the brain for energy so the brain cells have fuel for normal functioning. According to Robert Sapolsky in Why Zebras Don’t Get Ulcers, in prolonged stress, the amount of glucose sent to the brain drops by 25%. This makes it harder for the brain cells to function normally, and in particular it decreases their capacity to respond in times of neurological crisis, such as decreased oxygen supplies and other issues that can arise associated with stress. In effect you have a less resilient brain that is more susceptible to problems.
An additional effect is that, in fight or flight, blood flows only to one side of the brain, and brain function becomes one-sided. In normal functioning the two sides of the brain would constantly be working together to process information, each side picking up different and complementary pieces of information. For accurate information processing, the hemispheres of the brain would work together. One side dominance has an impact on comprehension, information processing and response, learning, and normal, healthy body functioning.
In the parasympathetic nervous system state, glucose transfer to the brain is able to return to normal, and blood flow is restored to both sides of the brain.