A pulsar is a neutron star left behind by a supernova, spinning extremely fast and carrying an intense magnetic field. As it rotates, it channels beams of radiation out from its magnetic poles, and because those poles rarely line up with its spin axis, the beam sweeps across space the way a lighthouse beam sweeps across the sea.
From Earth, that sweeping beam is picked up as a steady, precise pulse of radio waves each time it crosses our line of sight, some pulsars completing hundreds of rotations every second. Their timing is so exact that early pulsars were briefly mistaken for signals from another civilization.
Pulsars are now used as some of the most reliable natural clocks in the universe, precise enough that astronomers use networks of them to search for the faint ripple of gravitational waves passing through the galaxy. More on how they work is available from NASA’s Imagine the Universe.