Why is surgery necessary?
The mitral valve is the inflow valve into the left side of the heart. It closes during systole (when the ventricle  contracts or squeezes blood out into the aorta and the rest of the body). When the mitral valve leaks, blood flows backwards into the lungs.
The ventricle must therefore pump more blood with each contraction to produce the same forward output of blood throughout the body. This resulting condition is called a volume overload. The heart can compensate for this volume overload for many months or years (provided the leakage came on slowly and progressively), but it eventually begins to fail producing symptoms of shortness of breath or fatigue.