I have not yet had to have a blood transfusion, but I will echo other posters in that blood groups need to be fully understood and typed before transfusion is permitted. Although the incorrect blood group can cause problems, worse problems can be caused by indiscriminate transfusion of blood; Isaac Asimov died because he received a blood transfusion that had HIV in it. They didn't find out until later, when he developed AIDS, and then it was too late. We are fortunate that we have pretty good blood screening in the U.S.
ABO blood group is a division of blood types based upon differences in antigens. To illustrate, type O blood group has neither the A antigen nor the B antigen; AB groups are distinguished from each other by the presence of either the A antigen or the B antigen.
As added information to all of the above, Rh type of the mother is important in pregnancy. For example, if the mother is Rh-negative, and she is carrying a baby who is Rh-positive, the baby's blood cells can enter the mother's circulation during the pregnancy and and causse the mother to develop antibodies against Rh-positive cells. Once developed in the mother, these antibodies then can cross the placenta and destroy the Rh-positive red cells of the fetus. This causes hemolytic anemia in the fetus, and the baby may be born with severe anemia requiring transfusion.
Around 1900, Austrian Karl Landsteiner (1868-1943) discovered the ABO blood groups for which he won the Nobel Prize in Medicine; about forty years later, he and another scientist, American Alexander Wiener (1907-1976) discovered the Rh factors. For those who have had surgery or blood transfusions, be thankful for their work!
Over time, researchers have uncovered 45 different Rh "factors" associated with human blood. See more at the link:
The "Rh blood group" refers to the Rhesus factor, referring to a group of blood antigens that every individual either does or does not have on his/her red blood cells. When testing an individual prior to providing a blood transfusion, for example, it is important to determine the ABO group and the Rh presence or absence of the recipient and to match the donated blood to both groups.
The answers given above say almost everything that needs to be said from a scientific viewpoint about this topic. I will simply add a personal note. About three years ago I had major surgery and had to have blood transfusions. Fortunately, my wife has the kind of blood that is universally acceptable, and so she was the person whose blood was used during my surgery. She is constantly being called by blood banks who want her to donate (which she does) because her blood is especially valuable. I am very glad to have some of her blood mixed with mine!
Blood type O is the most common, and it is known as a universal donor because people with type O blood can donate to anyone. Type A and B are less common, and if you have one of those blood types you need the same blood type to donate or to get blood.
It is vital to understand the different blood types that people have precisely because it can be a matter of life or death for some people. As somebody who has had a few blood transfusions myself, it is very important that medical staff are able to identify the blood type of their patient and ensure they get blood from a similar match before giving the patient blood, otherwise great harm can be caused.
My impression is that it's important to understand these groups because you have to know what blood group someone has so that you can give them a transfusion if necessary. You can have a blood type of A, B, AB or O. Within those types, you can be RH negative or positive.