A pulsar is a dense, rotating object which gives off a beam of radiation from each of its magnetic poles. They come from neutron stars - the leftovers of a supernova. These recently exploded, massive stars, spin very fast and have a very strong magnetic field.
Pulsars emit beams of radio waves and other radiation. We can only detect them if the beam points towards Earth, so there may more be pulsars that we cannot observe. As the neutron star spins, the beams sweep past the Earth at regular intervals, or in pulses, hence the name. It's a bit like seeing the flashes of light from a lighthouse.
The amount of time between each pulse can be as long as 20 seconds and as short as a few thousandths of a second. This means some of these objects are spinning hundreds of times every second! This is incredibly fast when compared to the 24 hours it takes the Earth to rotate. Remember, these objects are the size of a city and contain as much mass as the Sun.
The first pulsar was discovered in 1967 by Jocelyn Bell Burnell and Antony Hewish. At first, they thought this regularly repeating radio signal could be from aliens! This led to them naming the first pulsar, LGM-1 (or Little Green Men 1). But they soon realized that this was not the case!
Studying pulsars helps us learn how physics works in neutron stars, some of the densest objects in the Universe. Their regular spin also means we can use them like clocks. If the amount of time between pulses changes, this tells us something is happening nearby in space. The first exoplanet was found in orbit around a pulsar. Pulsars have also been used to measure distances and detect ripples in the fabric of space-time.