Solid magnets (like the ones you are familiar with) have crystal-like sections of metal within them that "pretend" to have electric currents inside (they aren't intelligent, so can't really pretend as you would, but they do behave like they have electricity in them when they don't). These pretend currents exert a magnetic field, which exerts a force on other electric currents be they real or also pretend, and they also induce currents in non-magnets nearby, allowing them to create force.