What happens to gasoline when it lands on your hand?
It evaporates, but it will first take some hydrocarbon compounds in your skin

Gasoline is a mixture of a variety of volatile hydrocarbons, some branched chain alkanes and some aromatics. The warmth of your hand is enough to cause small quantities to evaporate. But it will also dissolve some of the hydrocarbon-soluble oils from your skin. Then when it evaporates, they will be left but they will form a microcrystalline powder rather than returning to the parts of the skin they were extracted from: this is the white residue. This is a common when volatile non-polar solvents are spilled on the skin (don't do it too much or your skin will be deprived of the oils that keep your skin flexible and impervious to outside contamination). Small quantities are nothing to worry about, just don't get into the habit or it will hurt your skin.