The sun is about 4.5 billion years old and it is estimated to still possess a 5-billion year supply of hydrogen (hydrogen is the fuel that drives nuclear fusion on the sun). Therefore, it is predicted that our sun will die in approximately 5 billion years. Once the sun has converted all its hydrogen into helium, the sun will change from its current form, a yellow dwarf, into a red giant. As a red giant, its diameter will extend well beyond the orbit of Venus, and even possibly beyond the orbit of Earth. When the sun enters the red giant phase, in which it will spend the final 10 percent of its lifetime, the Earth will be burned to a cinder.
Even if Earth would escape incineration in the Sun, still all its water will be boiled away and most of its atmosphere would escape into space. In fact, even during its current life in the main sequence, the Sun is gradually becoming more luminous (about 10% every 1 billion years), and its surface temperature is slowly rising. The Sun used to be fainter in the past, which is possibly the reason why life on Earth has only existed for about 1 billion years on land. The increase in solar temperatures is such that already in about a billion years, the surface of the Earth will become too hot for liquid water to exist, ending all terrestrial life.
Following the red giant phase, intense thermal pulsations will cause the Sun to throw off its outer layers, forming a planetary nebula. The only object that will remain after the outer layers are ejected is the extremely hot stellar core, which will slowly cool and fade as a white dwarf over many billions of years. This stellar evolution scenario is typical of low- to medium-mass stars.
Sources: Pasachoff, Jay M. Contemporary Astronomy, pp. 205-6; The Universal Almanac 1992, pp. 482-83.