Human blood is classified according to the presence or absence of certain proteins that act as antigens — that is, they would induce the production of antibodies if they were introduced into the blood of an individual whose red blood cells lack these proteins. For a transfusion to be successful, the donated blood must be exactly like the blood of the person who will receive it. If not, clots form in the recipient’s blood vessels, and death can occur.
Blood is classified into four groups: type A, type B, type AB and type O. If only protein (antigen) A is present, it is type A blood. If only protein B is present, the blood is type B. Blood with both A and B proteins is type AB. If neither A nor B proteins is present, the blood is type O.
A further complication is the presence or absence of yet another substance called the Rhesus or Rh factor, so named because it was first found in the red cells of Rhesus monkeys. It is present in 85% of humans and absent in 15%. Persons who have this substance are said to be Rh positive (Rh+). Persons without the substance are Rh negative (Rh-). An individual may have blood type A and be Rh positive. He or she is said to be A+ and can only receive blood from donors who have blood type A or O and also are Rh+. Persons with type O blood and who are Rh negative are O-, and can only receive blood from a person with type O, Rh negative blood. The rarest blood type is what is called Bombay blood, which only a few people have.
The accompanying image (above) indicates the blood type combinations that are safe for transfusions.
Blood type (Wikipedia)