Question

What is a pulsar?

Answer 1

A Pulsar (pulsating radio star) is a fast spinning neutron star which emits radio pulses.

At the end of their life, big stars (`>1.4 M_(Sun)`) start to contract (due to gravity) reducing their volume and in doing so reaching enormous densities. The stellar "corpse" is squeezed so tightly that electrons and protons fuse into neutrons leaving a ball of neutrons of diameter of few kilometres.
The structure of the neutron star is dominated by the extremely high density of its core giving a very high surface gravity and its extremely high magnetic field (`~10^8` Tesla).
A neutron star still rotates as when was still "alive" but now it is smaller so it has a high rotational energy that the high magnetic field of the neutron star itself can transform into electromagnetic radiation (Radio waves).
Two beams of radio waves are emitted along the magnetic axis of the rapidly rotating neutron star.

To an observer it seems that the beam pulsates at fixed intervals, because the neutron star, rotating about its rotational axis, makes the magnetic axis, along which is emitted the radio wave, rotate in a conical beacon-like pattern:

(Reference for supporting data and figures: Introductory Astronomy and Astrophysics - M. Zeilik, S. A. Gregory, E. v. P. Smith)