A red giant star is a dying star in the last stages of stellar evolution. Medium mass stars, like our Sun, live by fusing the hydrogen within their cores into helium. This is what our Sun is doing now. When the star runs out of hydrogen in its core to fuse, it then starts fusing the helium and remaining hydrogen in a shell surrounding the core. The energy produced by this fusion causes the star to expand outward to many times its original size. But now this outer envelope is lower in temperature, giving them a reddish hue and thus they are called Red Giants.
The Sun will only spend one billion years as a red giant, as opposed to nearly 10 billion years it spent busily burning hydrogen. In only a few billion years, our sun will turn into a red giant star, swell and engulf the inner planets, possibly even Earth. Red giant stars reach sizes of 100 to 1,000 times the size of the sun and a little over half as hot as the sun. In roughly 5 billion years, the sun will start the helium-burning process, transforming into a red giant star. When it will expand, its outer layers will consume Mercury and Venus, and reach Earth.