What is the advantage of multistage missiles over single-stage missiles?

When a rocket accelerates in flight, the stored energy of its fuel (fuel + oxidizer) is gradually converted into kinetic energy of the rocket. The transformation occurs at each moment of time, respectively, the greater the mass at a given moment of time the entire rocket has, the more energy must be expended in order to provide the same increase in its speed.
The use of multi-stage design allows you to drop empty fuel tanks in flight, thereby reducing the mass of the rocket in flight and thereby reducing the amount of energy spent on its acceleration.