When something happens out of the blue, it is a complete surprise. If you get a phone call out of the blue from an old friend, it's utterly unexpected.
Use the phrase out of the blue when you need a casual way to describe something that surprises you and possibly seems to come from nowhere. Your parents might announce, out of the blue, that they're moving to Mexico, for example. Another way to say out of the blue is from the clear blue sky. Both raise the image of something solid emerging magically from the sky.