The reason for the red giants and supergiant stars being the brightest stars in the sky is their large radius and mass leads to high temperature.
The red giant and supergiant stars, are stars with a relatively large radius relative to their mass and temperature. The brightness of such stars is high since the radiating surface is correspondingly large. A subclass of giant stars are supergiants that have larger radii and luminosities for mass and temperature. A very bright red giant with a low temperature. The subgiant has a slightly reduced radius and brightness.
There are giants that are hundreds of thousands of times brighter than the sun. Their position on the Hertzsprung-Russell diagram is above the main sequence, where most stars fall as opposed to dwarfs. Giants and supergiants can have masses 10 to 30 times that of the Sun, but their volumes are often 1 million to 10 million times that of the Sun. They are, therefore "diffuse" low-density stars.
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