Bacchus is the Roman name for the Greek god Dionysus. Dionysus was the son of the Greek god Zeus (or Jupiter, to use his Roman equivalent) and a mortal woman named Semele. Dionysus was the Greek god of wine, the grape harvest, ecstasy and madness.
According to Greek mythology, Zeus' wife Hera became so jealous after Zeus impregnated Semele that she tricked the mortal into asking to see some proof of his godhood. The lightning of Zeus' divine presence incinerated Semele. Zeus rescued their unborn child and sewed him into his thigh, and Dionysus was born from Zeus' thigh some time later.