It uses the lorentz force, when there is a magnetic field and an object that has current flowing through it perpendicular to the field this will generate a force perpendicular to both the magnetic field and the current direction.
In a railgun the projectile is usually part of a closed circuit, this means there is current going trough it, and because the circuit acts as a coil there is a magnetic field as well, so the lorentz force created from this propels the projectile.
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