A person wih blood group O is called a Universal Donor. Well, his plasma contains antibodies A and B. During blood donation, if blood group O is given to a person with blood group A (since blood group O can be donated to all the blood groups) then wouldn't the antibodies of the donor with blood group O harm the recipient? Although nowadays doctors prefer giving blood having 100 percent compatibility...
The key feature of type O blood as "universal donor" is that the incoming red blood cells have neither A nor B antigens and so the resident antibodies (anti-A , anti-B) will not react with them. Since transfusions are carried out with packed red blood cells the plasma antibodies of the donor don't matter - they will not be introduced into the recipient.
This is because the 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.