A pulsar is a rotating neutron star that emits electromagnetic radiation and charged particles from its magnetic poles. The rotational and magnetic axes are not necessarily aligned in a pulsar. As the pulsar spins about its rotational axis, at least one of the magnetic poles sweeps through the observer’s line of sight. When the magnetic pole is pointed towards the observer, increased light will be observed. When the magnetic pole is pointed away from the observer, the light will be considerably dimmer. As the pulsar spins, this creates the appearance that the neutron star is turning on and off, causing the light streaming out along the magnetic poles to appear pulsed (hence the name “pulsar”).
If neutron stars are made of neutral particles, how can they have magnetic fields?
Neutron stars are not totally made of neutrons-- the interiors have plenty of electrons, protons, and other particles. These charged particles can maintain the magnetic field. Plus, a basic property of magnetism is that once a magnetic field is made, it cannot simply disappear. Stars have magnetic fields because they are composed of plasma, very hot gas made of charged particles. When the star collapses to become a neutron star, it retains that “relic” magnetic field. And since the star gets smaller, the magnetic field gets stronger, since in a sense the field gets denser, more compressed. That is why neutron stars not only have magnetic fields, but why they are so strong.