A stiff back can be caused by many things including arthritis, back strain, alignment issues, and general stiffness. These back stretches should help.
Some great ways to relieve a stiff back are pelvic tilts, bridges, trunk rotation, single knee to chest, and double knee to chest. All these help loosen up the pelvic and hip muscles, as well as the back extensors and trunk muscles.
A prayer stretch or child’s pose, and a cat/dog or cat/cow do a great job of stretching the whole back and hips, as well as other parts of the body.