Muscle of your lower back are used to support your posture. They help you lift heavy objects and they protect your spine.
There are many ways to perform this exercise (i.e. on a stability ball, a machine etc.) but one of the most studied version is by simply lying prone (face down) on the floor.
To perform the prone back extension, lie on your stomach. Lift your chest, head and shoulders off of the ground without using your arms to help. This forces the muscles of your middle and lower back to do most of the work. As demonstrated in the video, your hands are placed at your forehead. You can also rest your forehead on your hands with your elbows pointed out. This will help support your head and neck and keep them in line with your spine.