It was a staple of early morality plays and other theater. When all seemed lost, God would arrive on the scene and solve everything. Usually God was dropped down from the ceiling using some kind of machinery, hence the expression.

It has come to be used as recognition of the author taking the easy way out to solve problems, rather than have the characters work things out themselves.

In storytelling (film, play, etc.), it means an illogical and/or improbable resolution to a storyline that goes totally outside the internal structure of the story. An example would be if in Harry Potter Book 7, Harry and Voldemort are dueling in their FINAL confrontation and a lightning bolt comes out of nowhere and vaporizes Voldy out of existence. Duel won; happy ending.

It is a power or event that arrives in the nick of time to solve a difficulty in a novel or play. I.e. providential intervention From the Latin “god from the machinery”, by which in ancient theatre gods were shown in air.