A star the size of the Sun will end its life after several billion years by expanding greatly because of changing energy balances at the core of the star. The surface temperature drops and the star becomes redder, this lasts several million years before the star throws off its outer layers and becomes a white dwarf. See also Dwarf star, Supergiant star.
As stars approach the end of their lives, the nuclear reactions that power them, change. This causes the star to greatly increase in size in a big way. A giant star has a similar mass to our Sun but is much larger and more luminous. The word giant is usually prefixed with the colour of the star e.g. red giant star.
A Giant star is a star that has stopped fusing hydrogen in its core. More specifically, the term giant star refers to a star that belongs to the luminosity class II or III in the Yerkes spectral classification. This means it lies above the main sequence (luminosity class V) on the Hertzsprung-Russell diagram.