It won't supernova. It's just a dwarf star. It expands because it runs out of hydrogen and begins to collapse which causes friction and therefore heat. The balance between gravity and heat pressure is upset and the star expands.
Yes, the Sun can expand during a phase of its life cycle called the "red giant" phase. As stars age, they exhaust their nuclear fuel (primarily hydrogen) in the core. When this happens, the core contracts while the outer layers expand due to the released energy from the contraction. This expansion causes the Sun to become a red giant, increasing in size and luminosity. During this phase, the Sun will expand to the point where it may engulf inner planets like Mercury, Venus, and possibly even Earth. Eventually, after the red giant phase, the Sun will shed its outer layers, forming a planetary nebula and leaving behind a dense leftover called a white dwarf.
