Stars are born and eventually die. But once deceased, they continue to exist, just in a different form. That final form depends upon their initial mass.
Because stars are so dense, gravity continuously compels them to contract and collapse in upon themselves. But stars are also very hot, a result of trillions and trillions (etc.) of atoms -- commonly hydrogen or helium -- fusing together, releasing massive amounts of energy in the process. This makes stars want to expand. So you see, a star's size is a delicate balance between crushing gravity and expanding fire.
But unlike gravity, nuclear fusion doesn't last forever. Eventually the star's fuel runs out. When this happens, almost all stars (including our sun) expand in volume over one hundred times, becoming red giants. This "last gasp," as astronomer Carl Sagan termed it, lasts a couple million years. That's actually pretty short compared to a star's ten-billion-year life cycle.
But after this fleeting expansion, contraction resumes. As eloquently described by Sagan in Cosmos, there are three ways for stars to die:
"A typical star with a mass like the sun will one day continue its collapse until its density becomes very high, and then the contraction is stopped by the mutual repulsion of the overcrowded electrons in its interior... A collapsed star that's held up by electron forces is called a white dwarf. It's a sun shrunk to the size of the Earth."
"A collapsing star twice as massive as the sun isn't stopped by the electron pressure and it goes on folding in on itself until nuclear forces come into play, and they hold up the weight of the star... A collapsed star supported by nuclear forces is called a neutron star. It's a sun shrunk to the size of a city."
"...a collapsing star three times as massive as the sun isn't stopped even by nuclear forces. There's no force known that can withstand this enormous compression. And such a star has an astonishing destiny. It continues to collapse until it vanishes utterly... A star so massive that in its final collapse it disappears altogether is called a black hole. It's a sun with no size at all."