It means he's a sovereign willing to hear and occasionally grant petitions from his subjects.
Of course, the hypothesis that prayer changes things is non-falsifiable.
https://s-media-cache-ak0.pinimg.com/564x/4f/6a/01/4f6a016cb8df899808674ff5fe3a0155.jpg
Your flowchart answers your previous question about the pointlessness of prayer.
Good things happen to good people = God's divine Grace!
Bad things happen to bad people = God's vengeance!
Bad things to good people = God's test of faith, or his unknowable mysterious ways!
Good things happen to bad people = God's mysterious ways, but the baddies will get their just desserts in the end!