Blood group O has antibodies against antigens A and B (Anti A antibody,Anti B antibody ). Blood group A has A antigen. If someone with blood group A receives donor blood with group O, then anti-A antibodies in the donor blood should attack the A antigens in the recipient's blood.
In reverse, Group A or Group B recipient's plasma contain soluble A or soluble B (antigen not bound to red cell surface). These free antigens will bind to the antibodies from the donors and prevent it to react on the red cell surface antigen A or B. The other thing is usually universal O should be low titer Anti-A or Anti-B.