In about 6 billion years the Sun's core will run out of hydrogen. When this happens the helium ash in the core will become unstable and collapse in on itself. The core will heat up and get denser as a result. The Sun will get bigger and enter the red giant phase. As a red giant it will begin the second stage of fusion at the core and will start burning helium and forming carbon. That phase will last about 100 million years until this source of fuel is burned up as well. The helium shell will become unstable causing the Sun to pulse and it will blow off a large fraction of its atmosphere into space over the course of several pulses. When its blasted off all its layers all that is left is the core of carbon. This is a white dwarf.