Alcohol is a depressant, which means it slows the activity of the brain. If someone abuses alcohol over a long period of time, their brain will adapt and create more and more sensitive reactive chemicals to try to retain normal brain function even in the presence of alcohol. This is called tolerance.
If the person were to suddenly quit drinking, the alcohol that was inhibiting brain reactions is no longer present, but the overly reactive chemicals are still there, meaning the brain is way more active than its supposed to be. This is a seizure. Think overloading a circuit with too much electricity – it burns out and misfires.