In the bottle, nitrocellulose reacts with the ethyl acetate to become a liquid. When you apply the paint onto your nails, the chemical solvent, ethyl acetate, burns off (aka the chemical smell), leaving behind the dry nitrocellulose
When the ethyl acetate burns off after applying it to your nails, the nitrocellulose is left behind, leaving it in its solid state. When nail polish remover is applied (aka the ethyl acetate), it turns the nitrocellulose back to its liquid state allowing it to come off the nails