UV rays are very harmful to living organisms because

UV rays are highly injurious to living organisms since DNA and proteins of living organisms preferentially absorb UV rays, and its high energy breaks the chemical bonds within these molecules. UV rays damages DNA and mutation may occur. It causes ageing of skin, damage to skin cells and various types of skin cancers.

UV rays help in the synthesis of vitamin D from 7-dehydrocholesterol in our skin. 

Ozone in the stratosphere acts as a shield absorbing ultraviolet radiation from the sun.

UV rays cause release of Cl from CFCs leading to the degradation of ozone.