The wear and tear theory of aging believes that the effects of aging are caused by damage done to cells and body systems over time. Essentially, these systems "wear out" due to use. Once they wear out, they can no longer function correctly.
A range of things can damage body systems. Exposure to radiation, toxins and ultraviolet light can damage our genes. The effects of our body's own functioning can also cause damage. When the body metabolizes oxygen, free radicals are produced that can cause damage to cells and tissues.
Not much. While the theory makes some sense if you think of the body as a machine, it doesn't really work when you realize the capacity of the body to repair damage. Of course, not all damage can be repaired fully, and mistakes in repairs may accumulate over time. A more likely explanation is that the decrease of functioning that is seen as "tear" in the "wear and tear" theory is really the result, not the cause, of aging.
Sources: How Do We Age? The American Federation of Aging Research
