In my simplified view, it comes down to GABA and NMDA receptors.
Alcohol promotes GABA receptors (which are neuroinhibitory receptors) and inhibits NMDA receptors (neuroexcitatory receptors). Chronic alcohol use upregulates both, but maintains a semblance of balance between the two.
Following alcohol withdrawal, the upregulated NMDA receptors are no longer inhibited by alcohol, so their overall activity increases. The GABA receptors are no longer being stimulated by alcohol. This imbalance of GABA and NMDA signals (with NMDA activity much greater than GABA activity) lowers the seizure threshold.
The acute management and prophylaxis of withdrawal-related seizures, therefore, is typically to promote GABA activity with benzodiazepines, thus restoring the balance between GABA and NMDA signals and increasing the seizure threshold.
Read more: Pharmacology and Nutritional Impact of Ethanol in Chapter 392: Alcohol and Alcoholism, Harrison’s Principles of Internal Medicine 18e.