Autophagy is when your body eats itself. That sounds pretty dramatic, but it is a good thing. There are a variety of systems in your body (part of the immune system) that patrol your own cells and make sure that cells are not damaged. When a damaged cell is found, it is eaten and the molecules recycled (nice to know that your body is "green").
What this accomplishes an it makes sure that there is not build up of damaged cells or molecules inside tissues and organs. If this system breaks down, then there is an increase in cellular "junk" in the body that can, eventually, interfere with the higher functioning of organs.
Researchers at the Albert Einstein College of Medicine just received a $10 million award from the NIH to study the processes of autophagy and learn what role autophagy has in aging (and if it can be manipulated.
Read More: Theories of Aging.