Every great mythological figure needs a cool birth story. (Don't ask us why. It's just required.) In this tale, we hear about how Dionysus first enters the world with a bang that unfortunately destroys his mother, and then must continue developing in his father Zeus's thigh before he's ready to finally crawl out into the world. So, in a way, he's born twice, once of a female and once of male. These themes of rebirth, as well as gender-bending, were pretty hard to avoid within the cults of Dionysus, so it makes sense that they'd be part of his origin story.
In some versions of the tale, Dionysus later goes to the Underworld to rescue the soul of his mother, Semele. When he gets her back to the world above, he transforms her into a goddess. Dionysus joins a very elite club of dudes who were able to travel to the Underworld and back successfully. By making this treacherous journey and taking his mother from death to immortality, Dionysus shows that he has a crazy amount of power over life and death. Initiates into Dionysus's cults were all about their resurrecting god, and some thought of themselves as being reborn after taking part in his wild, wine-fueled rites.