Stars are not static: they have a life-cycle.
A red giant is a star which has run out of material for nuclear fusion, cooled down, and turned red.
When fusion material runs out, the outward pressure from fusion no longer balances gravity, so the core of the star contracts, but any hydrogen outside the core heats and expands, fusing into helium.
This new phase of activity also shifts the star's visible light output into the red region, so that a "small" white star becomes a red "giant" star, to our eyes.
Anne Evans
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