In the stratosphere, oxygen can exist as ozone, or O3. Different wavelengths of ultraviolet (UV) light help combine and dissociate the ozone molecule by adding or removing atomic oxygen:
O + O2 + (<240nmUV) -> O3
O3 + (>290nmUV) -> O2 + O
The net effect of these reactions is that much of the high energy, or "hard"(greater than 290nm) UV light is absorbed, and little reaches the ground. This balance has existed for tens or possible hundreds of millions of years. The primordial Earth's atmosphere was not rich in oxygen; consequently much UV light penetrated to the surface, and was at first responsible for initiating chemical reactions we associate with life.
Chloroflorocarbons are compounds that contain chlorine, fluorine and carbon atoms, such as CFCl3 (one carbon, one fluorine, 3 chlorine.) With the advent of CFC's in air, however, the UV light first breaks those compounds apart, releasing Chlorine:
CFCl3 + (>290nmUV) -> CFCl2 + Cl
Which then reacts with Ozone:
Cl + O3 -> ClO + O2
ClO + O -> Cl + O2
The free chlorine atom is then free to attack another ozone molecule, so these last 2 equations continue indefinitely. One CFC molecule can destroy 100,000 ozone molecules. With decreased Ozone, more "hard" UV (>290nm) gets to Earth, and this radiation can disrupt bacteria and cellular function, altering the delicate biochemical balance, and creating problems.