Great question! The Sun is composed of ionized plasma, which is a soup of charged particles. By way of Maxwell's equations (namely, Ampere's law), the jostling/acceleration of those charged particles creates magnetic fields. There is a lot of interplay between the electric and magnetic fields depending on the local density, and "magnetic flux tubes" can be created under the right conditions which direct the particles along magnetic field lines. Concentrations of these flux tubes penetrating through the "surface", caused by the twisting and lifting of magnetic field lines from within much deeper layers of the sun, result in sunspots.