What does "hair of the dog that bit you" mean?

Whatever made you ill used as a remedy, especially alcohol as a hangover cure. For example, A little hair of the dog will cure that hangover in no time. This expression, already a proverb in John Heywood's 1546 compendium, is based on the ancient folk treatment for dogbite of putting a burnt hair of the dog on the wound. It is often shortened, as in the example.