Initially, the helium core simply contracts and heats while the hydrogen-burning shell expands. Eventually though, the (now degenerate) helium core reaches the temperature necessary for fusion. In stars of a few solar masses or less, helium fusion begins explosively, with pretty much the entire core "lighting up" at once. This releases a huge amount of energy, but not enough to blow the star up. In fact, lighting the helium core stabilizes the star, allowing it to shrink and heat up in a relatively brief, "clump giant" phase where it burns helium in its core and hydrogen in a surrounding. <br /><br />Inevitably, the helium core becomes choked with "ash" once again, only this time it's carbon and oxygen, with maybe some neon. The core collapses again, forming a degenerate center surrounded by a helium-fusing shell, and *another* hydrogen-fusing shell. This causes the star to swell up again to dimensions much larger than it was on the earlier red giant branch. Ultimately, failure to light the carbon-oxygen core causes the unstable interior to blow off the surrounding shells, creating a planetary nebula.<br /><br />For stars bigger than a few solar masses, helium fusion starts smoothly and evenly--there's no helium flash--and fusion progresses upwards towards various other elements. In the end though, gravity always wins.