A pulsar is a rapidly spinning neutron star that emits repeating pulses of energy towards Earth. They appear following a supernova, when the highly compressed core of a recently exploded, massive star is left spinning rapidly and with a very strong magnetic field.
Pulsars emit beams of electromagnetic radiation (light) that can only be detected if they are pointing towards Earth. Due to the rotation of the neutron star, 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 time separation between the pulses of a pulsar range from between 0.0014 seconds to 8.5 seconds. In other words, these objects are spinning incredibly fast when compared to the 24 hours it takes the Earth to rotate. In extreme cases, pulsars rotate at more than 500 times per second, and remember, these objects are around 30km across and can weigh as much as the Sun.
The first pulsar was observed in 1967 by Jocelyn Bell Burnell and Antony Hewish but due to the regular nature of the pulses observed, they wondered if they were a signal from an alien civilisation. This led to the first pulsar being named LGM-1 (or Little Green Men 1). We now know this is not the case.