Red blood cells can carry two main antigens: the A antigen, and the B antigen. Whatever antigens the DON'T have on their red cells, they will have antibodies against, in their serum (plasma). A person's blood group (or blood "type") is defined by the antigens present on their red cells. For example, someone with group A blood has the A antigen on their red cells, and anti-B antibody in their serum. This is why we have to be very careful about who gets what type of blood. If someone gets "out of type" blood, their antibodies will react against, and destroy the transfused red cells within the blood vessels, a process called "intravascular hemolysis." When red cells are destroyed within vessels, they release their contents to the entire body. Interestingly, the contents of red cells can be deadly when released like that, possibly causing renal failure (kidneys shut down), vascular collapse (the blood vessels lose their "tone" and can't support blood pressure). These things can lead to death.
Some of you may think those antibodies look funny, and compared to what people normally thing of with antibodies, they DO!! Most antibodies are a class called IgG, which look like a Y. These antibodies, the Anti-A and anti-B are of a class called IgM, which is made up of five IgG antibodies bundled together. This, along with their ability to "fix complement," are what allow anti-A and anti-B to destroy red blood cells within the vessels.