A star that exhausts the hydrogen at its core alters its appearance as it reconfigures itself to burn helium, carbon, and oxygen. As a group these stars are called red giants. A red giant tend to be massive because only stars more massive than about 0.4 times the Sun's mass can consume their core hydrogen supply in less than the age of the universe (no more than 18 billion years). It is a giant because the star is physically larger than it was during its main-sequence phase, and it is red because the surface temperature is lower than during the main-sequence phase to counter the effect of a larger surface area on the cooling of the star. Red giants are short-lived, and once thermonuclear fusion ceases in them, they cool to blackness as degenerate dwarfs and neutron stars, or they collapse to black holes.
As with most things in astrophysics, the observationally-driven red giant classification buries a tremendous amount of physics. While each main-sequence star is powered by a single process—thermonuclear fusion of hydrogen in their cores—a red giant star can be powered by a variety of thermonuclear processes at its cores and within shells surrounding the core. At the beginning of its red giant phase, the star burns helium at its core. Once this is exhausted, the star burns carbon. After the carbon is exhausted, the star burns oxygen. This march through the products of the previous stages of thermonuclear fusion continues until either electron degeneracy pressure stabilizes the star as a degenerate dwarf or until all of the nuclear fuel has burned to iron, at which point the star collapsed to either a neutron star or a black hole. Regardless of the fuel burned at its core, however, most of the energy produced by the star comes from burning hydrogen in the star's outer envelope.
The term red giant is relative. Massive stars in transition from core hydrogen burning to core helium burning have cooler photospheres than during their main-sequence phase, but they can still be hotter and bluer than the Sun. This is particularly true of very massive stars, which in their red giant phase form a class of objects called supergiants; these stars generate ten thousand times the power of the Sun, but can range in color from very blue to very red relative to the Sun.
The radius of a star's photosphere during the red giant phase is dramatically larger than it was during the main-sequence phase. For stars less than a couple of solar masses, this increase in radius counters the an increase of a factor of 10 or more in brightness. The low-mass stars do not become dramatically redder in their giant phase, so the larger surface area is simply to counter the greater power generation. A solar mass star increases its radius by roughly a factor of 6 as it moves into its giant phase, while its temperature drops by only about 35%. This gives a solar-mass star a radius of about 0.03 AU. When the sun becomes a red-giant star in four billion years, its photosphere will remain inside the orbit of Mercury. From Earth, the Sun in this phase would have a diameter of 3° on the sky, versus the current 0.5°.
Large stars change more dramatically in appearance as they evolve into red giants than do the small stars. In the transition from the main sequence to core helium burning, a star of 9 solar masses reddens dramatically, going from a photospheric temperature of 30,000° to a temperature of 2,500°. This minimum temperature of around 2,500° is a feature of giant stars of all masses. Unlike a low-mass star, a high mass star becomes only modestly more luminous, so the factor of 12 in temperature for a 9 solar mass star is accompanied by a factor of 4 increase in photospheric radius. The transition of a massive star from high temperature to low temperature produces the variety of colors seen among the supergiants.
The reddest bright stars we see in the sky with our eyes are all red giants. This is because they are much brighter than the red, low-mass main-sequence stars. Betelgeuse, the bright red star in the Orion constellation, is the most prominent example of a red giant (in fact, a red supergiant) in our sky. This variable star is among the brightest stars in our sky, with an apparent magnitude of around 0.5, but it is also a very distant 470 parsecs from us. This star generates more than one hundred thousand times the power of the Sun. It is also among the reddest stars in our sky. Almost as luminous, but somewhat closer to us is the supergiant Antares, the brightest star in Scorpio. Antares is around 170 parsecs from us. With an apparent magnitude of around 1, it is ten thousand times as luminous as the Sun.
More in the red giant range are stars such as Arcturus and Aldebaran. These stars are much less luminous, but much closer, than either Betelgeuse or Antares. Arcturus, the brightest star of the constellation Bootes, is 10 parsecs away; it generates less than 100 times the power of the Sun, giving it an apparent magnitude of 0. Aldebaran, the brightest star of the constellation Taurus, is 19 parsecs away; it generates 100 times the power of the Sun, giving it an apparent magnitude of 0.9.