The Sun that we circle year after year follows a life cycle that is the same throughout the solar system. The cycle has several stages with our Sun around 4.57 billion years old. This puts our Sun half way through its "main-sequence" evolution, during which nuclear fusion reactions in its core fuse hydrogen into helium.
Each second over 4 million tonnes of matter is converted into energy within the Suns core. The sun will spend around 10 billion years as a main sequence star.
The Sun does not yet have enough mass to explode into a supernova, instead in 4-5 billion years it will enter a red giant phase with its outer layers expanding and its core heating up. Helium fusion will begin when the core reaches around 100MK, and will produce oxygen and carbon. Entering the asymptotic giant branch of a planetary nebula phase in about 7.8 billion years, during which instabilities in interior temperature lead the surface of the sun to shed mass. While it is likely that the expansion of the outer layers of the Sun will reach the current position of Earth's orbit, recent research suggests that mass lost from the Sun earlier in its red giant phase will cause the Earth's orbit to move further out, preventing it from being engulfed. However, Earth's water will be boiled away and most of its atmosphere will escape into space. The increase in solar temperatures over this period is sufficient that by about 500-700 million years into the future, the surface of the Earth will become too hot for the survival of life as we know it.
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.
Refer to the picture above for a pictorial explanation.