According to some:
The Sun is a pretty ordinary star. Middle of the road in what astronomers call the "Main Sequence" O,B,A,F,G,K,M (our sun is a G star).
It is about half way through its life cycle and has about 5 billion years to go. Its mass is too small for it to explode (Nova) or to implode. Star 1.5 to 2 times our sun can implode and become neutron stars. Our sun will become a red giant and expand way beyond the earth's orbit.
Eventually it will eject the outer layer of material and the sun will become a white dwarf star.
What about explode:
No, the Sun will not explode. To explode indicates that the internal forces will eventually overcome gravity and violently tear the Sun apart. This is not the fate in store for the Sun. As Clark described, the Sun will eventually start to burn helium to produce Carbon. However, that is as far as it will go. The Sun does not have enough mass to generate the heat required to burn carbon to produce heavier elements. As helium builds up in the Sun's core, the hydrogen fusion will move to higher levels in the Sun. This will more strongly heat the outer layers of the Sun causing them to expand. (This is not an explosion.) The Sun will eventually expand to swallow Earth and possibly even Mars. At the same time the core will contract raising the temperature until helium fuses to produce Carbon. The Helium will be burned up fairly quickly. Once it is gone, the core will begin to collapse down to a white dwarf and the outer layers will relatively quietly separate from the core and move outward to form a planetary nebula (http://tinyurl.com/dhsej). This is the fate that awaits the sun.
FYI, when astronomers talk about a star exploding, they are usually talking about some sort of nova or supernova. The Sun has nowhere near enough mass to do that.
or here: In nucleosynthesis, when all the hydrogen atoms are fused into helium atoms, could the helium atoms fuse into something, rather than the Sun turning into a white dwarf?
Stars like the Sun burn hydrogen into helium in their centers during the main-sequence phase, but eventually there is not enough hydrogen left in the center to provide the necessary radiation pressure to balance gravity. The center of the star thus contracts until it is hot enough for helium to be converted into carbon. The hydrogen in a shell continues to burn into helium, but the outer layers of the star have to expand in order to conserve energy. This makes the star appear brighter and cooler, and it becomes a red giant.
During the red giant phase, a star often loses a lot of its outer layers which are blown away by the radiation coming from below. Eventually, in the more massive stars of the group, the carbon may burn to even heavier elements, but ourSunwill never really get past carbon. Eventually the energy generation will fizzle out and the star will collapse to a white dwarf.
