This phrase is a metaphor where 'heavens' refers to the sky and does not imply a religious meaning. At the festival, the heavens opened up, but the band played on.
Pro Tip 2/3
Sudden Change
The phrase often conveys a sudden or unexpected start to heavy rain. During the match, the heavens opened, stopping the game.
Pro Tip 3/3
Dramatic Effect
It's used for dramatic emphasis to describe a particularly heavy downpour. I forgot my umbrella, and then the heavens opened on my way home.