What does it mean if you start getting double vision when you're intoxicated?

Loss of control. There is a condition called a phoria, which occurs when people who have otherwise straight eyes get tired or have decreased consciousness (or get drunk). The eyes "cross" temporarily but can be forced to straighten with effort. There is no danger, but it is a definite sign that you are intoxicated.
Stop drinking. Probably pretty well intoxicated, and may even black out.
Decreased function. Your brain, specifically the brainstem where eye muscle control occurs, is getting supressed by the amount of alcohol in your bloodstream. When you discontinue driinking, the double vision should dissapear. Higher levels of intoxication are associated with double vision, so your entire brain is being affected as well.