The vertebrae in your spine are a stack of bones. This stack naturally curves in at your lower back. Between each vertebra is a disk. This disk is like a jelly doughnut, strong on the outside, and full of jelly in the middle. As long as your vertebra stay in their normal position, the jelly in the disk evenly fill the space between the vertebra.
Once you lean forward, the vertebrae push all the jelly to the rear. This bulge of jelly compresses the nerves that exit the spine. This nerve thinks that it is being told to contract the muscles in the lower back, and so it tightens up your back. The muscles pull the vertebra further out of line and the jelly gets pushed further back against the nerves. You now have a vicious circle. The constantly contracted muscles start to ache.
The same nerve that runs out of the spine also runs down the leg to the foot. Soon the buttocks, leg and foot start to ache. In its worst form, the jelly doughnut can rupture, and surgery is required to remove the excess material and repair the wall of the disk. Proper lumbar support is part of the prevention.