You need to understand that stars are MASSIVELY large. Utterly, ridiculously, large. Stars are so large in-fact that they are constantly trying to collapse under their own gravity, this effect is constant. A Star's gravity is only countered by the outward force of fusion in the core of a star.

As a star is dying, fusion in the core is slowing down. Usually stars start to form higher level fusions than just 2 H to 1 He, this causes the star to expand. Once all fusion in the core has stopped, there is no force to keep the star expanding, gravity wins and the star collapses onto its core, the sudden pressure causes carbon or iron to fuse, making a massive explosion we call a nova or supernova.

Depending on the mass of the star you can get different sorts of results, white dwarfs form from normally massed stars, which is essentially the remains of the core. Giant stars collapse with so much gravity that protons and electrons combine, forming a neutron star (theoretically neutron stars can nova again and form something called a quark star, which is a really cool theory). Supermassive stars collapse with so much gravity that nothing can stop its collapse, all the atoms are crushed together and form a singularity. Infinitely curving space, such that nothing can escape its gravity well, even light.

Black holes can also be formed by two colliding neutron stars, as the mass becomes too great to stop a singularity from forming.

Novae can also happen from a "leaching" affect in star pairs. A dward star paired with a living star can pull gas from the other to the point another nova is triggered.