A serum grouping result for ABO testing shows hemolysis. Why?

Answer 1

It simply means red cell incompatibility. There are many different blood groups with specific antigens. Hemolysis would mean cell destruction due to an existing antigen and antibody reaction with incompatible blood types.
Check out this wiki page for details:
http://en.wikipedia.org/wiki/Blood_type#Red_blood_cell_compatibility

Answer 2

"O" group people quite often have hemolysins - their anti-a and anti-b will hemolyse the test cells. That is why ABO incompatibilities of a fetus with an "O" mother can be very dangerous.