Zeus was married to his sister Hera, who expected her husband to prove faithful. Time and again, Zeus failed to live up to Hera's expectation. Since she was a goddess, Hera was more powerful than mortal women and used a sort of passive-aggressive pattern of behavior to punish her husband. Hera learned that Zeus had impregnated yet another woman, so Hera tricked the woman into asking Zeus to do something for her that would prove fatal. Zeus was obliged to give Semele whatever she asked for, so when Semele, on Hera's say-so, asked the god to reveal himself in all his glory, Zeus did so, and unintentionally, but unavoidably, destroyed Semele with his lightning bolts.
Before Semele's unborn child could be destroyed by the flames taking his mother, Zeus snatched the fetus and sewed him in his leg. That was Dionysus' first birth. The second came when Dionysus emerged at term from the thigh of Zeus.
Semele is also known as Thyone. Dionysus retrieved her from the Underworld and brought her to Olympus where she was known as Thyone, goddess of inspired frenzy [source: Theoi - Thyone].