Gluten has been shown to increase levels of the protein zonulin in the gut leading to leaky gut syndrome. This gut permeability allows undigested food proteins and bacterial endotoxins to pass into the blood stream, activating an inflammatory-immune response in your body.
Elevated zonulin levels in the gut have been linked to elevated zonulin levels in the brain. Translation: A leaky gut can lead to a leaky brain. Once the blood-brain barrier has been breached, your brains immune system — glial cells — can be activated. Glial cells will then cause inflammatory cascades throughout the brain. (I cover this topic in more detail in Signs You Might Have A "Leaky Brain" + What To Do About It.)