Nail polish chemistry question
Mixtures of water with flammable liquids can themselves be flammable, largely due to the fact that the flammable liquids generally are more volatile than water, (ie they evaporate more easily.) As a result, the air above a solution of nail polish will have a lot of molecules of the flammable liquid in it. (That's why you can smell them easily). If you have a flame near the liquid, those molecules in the air above it can combust. The heat generated will evaporate more liquid, which will fuel the fire. Some of the heat is lost to vaporizing water, which doesn't burn, but if the fraction of the total liquid that is flammable is high enough, the combustion continues.

In nail polish, the flammable liquid is usually acetone or ethyl acetate.