How does visualization promote relaxation and stress reduction?

Well, to most, it helps to remove ones thoughts from where you are at the present time. So it can help by giving a healthy escape, rather than falling to harmful things to take your mind off things. It can also help keep you in a more patient, and realistic, while still staying more positive. It is a lot like meditation in some ways, imagining yourself elsewhere, somewhere nice, comfortable, where you can simply relax. Imagining yourself in such a place can help you to relax in the here and now, in the midst of chaos.
I hope this helped!