I will assume you are asking about how nail polish remover actually removes nail polish.
Nail polish remover is mainly composed of acetone or other organic solvents. The action of nail polish remover is actually not a chemical reaction at all.Most nail polish also contains acetone or other organic solvents as a main ingredient. As nail polish dries, the organic solvent evaporates, leaving behind the film of coloring. Because this film is made to be dissolved in organic substances, it does not dissolve in water and therefore is not readily removed by handwashing. Nail polish remover simply re-dissolves the dried nail polish, returning the dried, colored film to liquid form. This makes it easy to simply wipe off the nail polish.