The horizontal branch (HB) is a grouping of stars (HB stars) on the H-R diagram that form a horizontal line on the diagram, leading away from the red-giant branch (RGB). They are generally red (red giants), but small giants (subgiants).
HB stars have passed through the RGB (for which they needed at least half a solar mass as main sequence stars) and have begun helium fusion (triple alpha process) in the core, with a surrounding shell of hydrogen fusion.
Their horizontal grouping in the diagram indicates their luminosity is similar despite varying colors, the latter of which reflects temperature. Not all stars produce these varying colors: depending upon metallicity, some (the higher metallicity stars) remain at a specific temperature, forming a group of stars in a small region of the diagram known as the red clump at the cooler end of the HB line.
After the horizontal branch (or red clump) stage, a core of carbon (product of the triple-alpha fusion) has accumulated to the point that the helium fusion is in a surrounding shell, and they enter the asymptotic giant branch (AGB) stage.