Every star in our universe has a beginning and an ending. New stars are formed from the remnants of the old ones and this cycle continues ahead. The star that dies out goes through a massive explosion which we also call as a supernova explosion. Depending upon it's mass, the star turns into black hole, white dwarf or "neutron stars". Stars weighing about eight times or more the mass of our Sun have a potential to end up as neutron stars. In it's early stages, a neutron star has a very high spin rate much faster than the rotation of a helicopter rotor! The extend of a neutron star can be as small as a small town, still we are able to see them due to some of their peculiar properties detectable by radio as well as X-Ray telescopes.
When a star having potential to form a neutron star burns out all it's fuel, the gravitational pull of the star crushes down all the gas & matter left in the star into it's core. The size of the star gets reduced to that of a city however, its density increases insanely! A teaspoon of this neutron star would weigh billions of tons! The collapse of the star results into a massive supernova leaving behind a dense star core having a very high rotational velocity the reason behind which is conservation of momentum since all mass of the star is concentrated in such a dense structure. This collapse results into generation of a very strong magnetosphere having magnetic strength millions of time stronger than that on Earth. The poles of this magnetosphere emit beams of highly charged particles, the science behind which is not completely understood yet.
As the star spins, the beams of charged particles also sweep a rotational curve. The magnetic and spin axes are not aligned to each other. Thus, whenever the beams of the spinning star cross our line of sight we receive a pulse of signal. As we continue to observe, we would get a train of pulses coming from the source. Therefore, a neutron star is also called as a "Pulsar" which stands for 'pulsating star'.
The first detection of a Pulsar was done by Jocelyn Bell and Anthony Hewish in 1967 while they were studying distant galaxies. Jocelyn Bell noticed small pulses of radiation when their telescope was looking at a particular position in the sky and for a short time scientists thought they might be coming from an extra-terrestrial civilisation. In fact the source of these pulses were initially referred to as LGM1, Little Green Man 1. Once established that the signals were not of this origin (and also not caused by people on Earth), the unidentified object they were coming from was called a "pulsar" because the emission was pulsed. The pulsar discovered by Bell and Hewish is now called PSR B1919+21: PSR stands for Pulsating Source of Radio and B1919+21 indicates the position of the pulsar in the sky.
As I mentioned earlier, pulsars possess highly accurate time period of rotation and so does the beam of charged particles coming out through the poles of its magnetosphere. However, as these pulsar beam signals travel through interstellar medium they undergo propagation effects which delays the time of arrival of these pulses. Once corrected for these errors, we can get a graph of highly timed pulsating signals as shown in the figure. The spin periods of pulsar are so accurate that they are also used for balancing atomic clocks here on Earth.
Pulsars & General Relativity:
Pulsars often exists as a binary pair with either a dwarf star or even an another pulsar. The properties of the orbit of this binary system can be determined through pulsar timing studies of the pulsar.
According to General Relativity, a binary system of stars emit gravitational waves and lose their energy thus shrinking their orbit. This effect is negligible in binary system of ordinary stars. However, for high energy binary system consisting of pulsars, the effect becomes significant and can be tested for theory of gravitational waves proposed by General Relativity. Observations of such systems have given satisfactory results till date with accuracy reaching upto 0.04%. Thus, the Theory of General Relativity will hold its ground as long as we find out more and more observational evidences with high amount of accuracy.