Alcohol dilutes your blood (i.e., makes it less dense) because alcohol is lighter than water. Alcohol-soaked blood builds up more quickly in your ears than elsewhere in the body, and that throws off this jelly-like structure in your ears called cupula. Effectively, it makes the cupula want to float. As they float, they bend. This sends signals to your brain giving you the illusion that your center of gravity is changing. Because this signal is constant, it makes you feel like the acceleration is going faster and faster. This results in the dizziness feeling that throws you off-balance.
To make matters worse, once the alcohol starts to leave your blood after many hours, the whole process happens in reverse. That's why you feel dizzy during a hangover.