In 1967, Jocelyn Bell Burnell and Antony Hewish observed, in the night sky, strong radio pulses separated by 1.33 seconds, like some sort of cosmic alarm clock. While these radio bursts were all but certain to be natural, the source was named Little Green Men-1, or LGM-1. What Burnell and Hewish had, in fact, observed was what has come to be called a pulsar.
But what, exactly, is a pulsar? Well, superficially, they're celestial objects which emit high-energy radio pulses in the X-Ray or Gamma region of the EM spectrum at rapid, regular intervals. What those celestial bodies were, in actuality, was a bit more complicated to pin down. There were a flurry of papers following the 1967 observation by the likes of Pacini, Bell, Gold, Goldreich, and Julian that began to pin down the nature of the beast, and they culminated in the first modern model of a pulsar by Sturrock in 1970. What all these papers suggested and built upon, proposed independently by both Franci Pacini and Thomas Gold, was that these pulsars were really rapidly rotating neutron stars.
We may need to back up a bit. What exactly is a neutron star? When a star has exhausted all of its viable fuel, and begins losing energy to fusion, it can collapse into one of three stable states. If it is a star like our sun, or even one up to 1.4 times as massive as our sun (in physics, known as 1.4 solar masses, and written 1.4☉), it will collapse into a white dwarf. This is a significantly smaller star that is held up now against the force of gravity by what is known as electron degeneracy pressure, which is, in simple terms, outward pressure caused by electrons in atoms not wanting to be smooshed together. If the star was originally much more massive than 1.4 times the mass of our sun, then gravity will overcome all other forces, and it will collapse down into a single point of zero volume and infinite density known as a singularity, or more colloquially as a black hole. However, if the original mass of the star is just above that 1.4 solar masses (which, incidentally, that 1.4☉ is known as the Chandrasekhar limit), then gravity, while strong enough to overcome electron degeneracy pressure and smoosh all the electrons in each atom down into their respective nucleus, is not strong enough to overcome neutron degeneracy pressure. This is a pressure that arises from nucleons themselves (the bosons that make up the nucleus of an atom—protons and neutrons) from overlapping. At this point, the entire star becomes one giant atomic nucleus made up of only neutrons, as all the electrons have been smooshed into the protons and become neutrons as well (yes, that is a thing that happens, and it's a bit more complicated than that, but we're going with that explanation for now). Now, this 20-kilometer (12.5 mile) wide, super-dense star which is one giant atomic nucleus made of neutrons, held together by gravity and kept from collapsing by the fundamental forces of the universe that really, really don't like it when bosons occupy the same physical space, is called a neutron star.
As these stars form as a result of supernovae, there's a lot of energy and paticulate matter that is ejected in the process. To form a pulsar, as the star collapses into a neutron star, it needs to begin to rotate, and as its radius shrinks and it throws off more matrial, that rotation speed becomes faster and faster, until the period of its rotation is measured in seconds or less. During this collapse, it also picks up a very strong magnetic field (I'll get into how later), and the combination of this absolutely mad roation and the magnetic field means that it throws off killer X-Ray or Gamma emissions (and by "killer," I mean literally killer. If there were a pulsar within a few light-years of us, the emissions would wipe out all life on Earth). A fun side effect of this crazy magnetic field and rotation is that anything getting too close to a pulsar would be shredded at the atomic level, with their protons and electrons being ripped apart. Not that anything, living or robotic, could even get that close while still functioning, because the EM emissions would fry them long before that.
So that's what a pulsar is: the decaying husk of a star not quite big enough to collapse into a black hole spinning through the remnants of its own demise all the while screaming lethal electromagnetic radiation into the void.
Eventually they do slow down enough that the EM bursts stop, and they go from "pulsar" to "neutron star." But at that point I lose a lot of interest in them.
...I don't really, neutron stars are super neat, but I really don't have enough time to get into why today.