Short answers, pulled from the story.
A giant star has a substantially larger radius and luminosity than a main-sequence star of the same surface temperature. Giant stars can have radii up to a few hundred times the Sun and luminosities over 10 times that of the Sun, placing them above the main sequence on the Hertzsprung-Russell diagram in luminosity classes II and III.
The Danish astronomer Ejnar Hertzsprung coined the terms "giant" and "dwarf" in 1905 or 1906. He introduced them to distinguish stars of quite different luminosity that share similar surface temperatures, particularly among K- and M-type stars.
A star becomes a red giant after the hydrogen at its core is depleted and fusion moves to a shell surrounding an inert helium core. The outer layers expand dramatically, luminosity surges after the core hits the Schonberg-Chandrasekhar limit and collapses, and the star moves onto the red-giant branch. A Sun-like star spends roughly 10 percent of its entire life on this branch.
The asymptotic giant branch is a late evolutionary stage where a star has exhausted its core helium and burns helium and hydrogen in surrounding shells around a degenerate carbon-oxygen core. Stars remain on the AGB for only around a million years before exhausting their fuel, passing through a planetary nebula phase, and becoming a carbon-oxygen white dwarf.
The helium flash occurs when a degenerate stellar core reaches about 100 million Kelvin and helium ignites explosively. Most of the released energy goes into lifting the degeneracy of the core rather than expanding the star; the core becomes convective, and the star's overall luminosity actually decreases as it moves from the red-giant branch to the horizontal branch.
Giant stars are grouped by temperature into red giants (spectral classes K, M, S, C, and some G), yellow giants (classes G, F, and some A), and blue giants (classes O, B, and sometimes early A). Red giants are by far the most numerous, with well-known examples including Arcturus, Aldebaran, and Mira. Yellow giants include pulsating variables such as RR Lyrae and W Virginis stars, while blue giants range from massive stars newly off the main sequence to low-mass horizontal-branch stars.