A red giant is a classification or type of star.
It is called a red giant because it radiates more light in the red part of the visible spectrum than most stars due to its low surface temperature and is a giant-sized star when compared to average stars like the Sun.
Towards the end of a star's life, the temperature near the core rises and this causes the size of the star to expand. This is the fate of the Sun in about 5 billion years. Stars convert hydrogen to helium to produce light (and other radiation). As time progresses, the heavier helium sinks to the center of the star, with a shell of hydrogen around this helium center core. The hydrogen is depleted so it no longer generates enough energy and pressure to support the outer layers of the star. As the star collapses, the pressure and temperature rise until it is high enough for helium to fuse into carbon, i.e. helium burning begins. To radiate the energy produced by the helium burning, the star expands into a red giant.