What does it mean when a vanilla label says “two-fold,” “three-fold,” “four-fold,” etc.?

This is an indication of the product’s intensity and concentration. With extract, for example, rules dictate how many vanilla beans must be used to make 1 gallon of extract (in the United States, that amount is at least 13.35 ounces). So, there is twice that weight of beans in a batch of two-fold vanilla extract, three times the weight in three-fold extract, and so on. Most pure vanilla extracts are single-fold; food manufacturers tend to use higher concentrations. But if you do come across a highly concentrated specialty vanilla product, you may want to reduce slightly the amount that a recipe calls for, to keep it from becoming overpowering.