That stars form is obvious - the universe is loaded with them. That stars have a finite lifetime and ultimately die is not so obvious. The process takes so long that we cannot watch it happen.
Chapter 11 mentioned that O and B type stars disappear from clusters much faster than Sun-like stars, implying that these massive stars have shorter lifetimes. That they do is not hard to demonstrate. Suppose you have a 10 solar-mass star; it will be something like 10,000 times as luminous as the Sun. It has 10 times the mass but burns it 10,000 times faster, so it will last only 1/1000 of the Sun's lifetime. The Sun has an expected total lifetime of 10 billion years, so such a 10 solar-mass star might last about 10 million years.
Here's a good graphic showing stellar lifetimes versus stellar mass.
Once a star begins burning hydrogen and stabilizes, it occupies its place on the Main Sequence. Massive (type O) stars lie at the top left and low-mass (type M) lie at the bottom left. The Sun is in the middle. The star's Main Sequence lifetime begins. Please note that the Main Sequence is NOT an evolutionary path for stars. A G-type star does not evolve to become an A-type star. The star remains close to its starting position on the Main Sequence for the duration of its hydrogen-burning life.
The star is in hydrostatic equilibrium, which means that the inward pressure of gravity and the outward pressure from the burning core are in balance all through the star. As long as these forces are balanced, the star is stable.
As the star consumes its hydrogen, it produces an "ash" in the form of helium. Helium is heavier than hydrogen, so it sinks to the center of the star and stays there (in a Sun-like star). As the star burns its hydrogen, this helium core expands. Look at Figure 12.2. This shows what happens to the composition of the gases in the star over time.
This helium core is very hot (formed by hydrogen fusion) and is NOT burning. Mass produces gravity, so the helium core compresses itself with its own gravity. As you already know, compressing a gas makes it heat up. This helium core heats itself up even hotter than the overlying hydrogen-burning region. This makes the hydrogen burn more rapidly, and the energy output increases. This, obviously, makes the star more luminous.
Now go back to section 12.1 and think about hydrostatic equilibrium. Increased energy output from the core upsets the equilibrium and pushes the outer envelope of the star outward, making it get larger. As the helium core gets larger (as it must), output increases and expansion continues. The star is leaving the Main Sequence and is heading toward the red giant stage. For the Sun, this change will take about 100 million years.
There are two things of interest in these stages. First - notice on page 333 where the size and density of the helium core are described. Think about the density of the shrinking core. Second - consider how a star which is beconing more luminous is, at the same time, getting cooler! How does this work? Our authors use an example of Arcturus. Its radius is currently 23 times that of the Sun and its luminosity is 100 times the Sun's. The surface area of a sphere proportional to the square of the radius, so a star of 23 solar radii has an area 529 times the Sun's. The luminosity of Arcturus is 100 times the Sun, so each square meter of Arcturus photosphere radiates about 1/5 as much as a square meter of the Sun's photosphere. Arcturus can radiate that greatly increased energy at a lower temperature.
Once the star's helium core gets big enough, its temperature will reach the level required to ignite helium burning. At this point the star changes again. The VERY dense core will expand, cool a bit, and settle down to helium burning. The energy output now decreases and the star arrives on the horizontal branch for a while.
Be sure you are carefully studying the excellent graphics showing the changing state of the star as it goes through the different stages and moves on the H-R diagram.
There are two ways that helium burning can start. If the helium core is degenerate, the burning starts explosively with the "helium flash". In larger stars, the core is hotter and not degenerate, so the burning of helium starts more smoothly.
In any case, once helium burning starts, carbon is produced and collects in the center.
We just said that the helium core of a Sun-like star can get so dense that it becomes degenerate. What does that mean? In the core, the electrons have all been stripped from the nuclei by the high temperature and make a sort of "electron gas" in the core. These electrons can only be squeezed together so far. When the Exclusion Principle comes into play, quantum forces prevent any further compression. This state of matter can resist enormous compressive forces, and stops the gravitational collapse and associated energy release.
This graphic shows the differences between normal matter and degenerate matter.
At stage 12, the core is so energetic that the radiation pressure drives the outer layers of the star off into space. The star separates into two components: the outer envelope and the core. The envelope expands into space and produces a planetary nebula (see the pictures on p. 319) while the core, relieved of the overburden, expands a bit, cools, stops burning, and settles down into existence as a white dwarf.