A Red Giant is a type of star that has fused all the hydrogen in its core to helium so nuclear reactions in the core have stopped. At that stage nuclear activity starts in outer layers of the star and the star swells to giant size. The light emitting layers of the star cool down till the star emits mainly red light. Red giants are very large and very luminous but the red giant faze in the lifetime of a star last a relatively short time, red giants last thousands of years which is long for human beings but far shorter than the previous life of the star on the Main sequence
Red giants should not be confused with Red dwarf stars though the names and the spectra of these two different types of stars are superficially similar, both have a similar red colour. Red dwarfs are small, faint, stable long lived stars.