The term red-giant branch (RGB) is a grouping of stars (RGB stars) on the H-R diagram that form a line on the diagram, leading away from the main sequence, consisting of stars in a phase soon after the main sequence phase. It includes some of the red giants (i.e., very bright, reddish stars).
RGB stars are stars with a helium core that is not burning, surrounded by hydrogen undergoing fusion (a hydrogen-burning shell). (Only stars with a mass of about a half solar mass minimum undergo this stage: smaller stars, red dwarves, keep mixing their helium and hydrogen due to convection.) Spectrally, the RGB stars have become K-type stars or M-type stars, but are much brighter than main sequence stars in those classes, with larger radii, i.e., giant stars or subgiants.
Their brightness is due to their greater energy production, more than during their main-sequence phase, due to the region of hydrogen fusion being larger. Their energy production is within the main-sequence B-class range, but red giants grow much larger than B-type main-sequence stars. I assume that is because the less massive star has less gravity counteracting the same outward radiation pressure due to the "B-type luminosity". Given this larger size, the energy spreads out to a larger surface than that of a B-type star, giving them a cooler photosphere and a redder color.
The RGB phase ends when helium fusion begins and the star enters a phase termed the horizontal branch (HB) (or red clump if they are not of varying color, generally stars of certain main-sequence spectral classes and with substantial metallicity).