What Is PURPLE RAIN?

I remember when PURPLE RAIN, the Movie, came out some 20 years ago. But I only this year saw it.

The film was okay, but nothing special. Prince plays a young Minnesota rock singer struggling to "make it" in the music industry without "selling out" his musical vision. At the same time, he's struggling with his personal issues: his father's abusive past and his own sexist attitudes.

In the end, Prince "makes it" while maintaining his integrity, he comes to terms with his father, and he learns to be more sensitive to women.

The strength of the film is not the story, but the music, which is quite good. But MY BIG QUESTION: Just WHAT IS PURPLE RAIN?

I've listened to the lyrics, and I can't figure it out. Is it a metaphor for something? If so, for what? Or did he just call it Purple Rain because it sounded like a cool thing?