A person with A+ blood receives B+ blood. The B antibodies in the A+ blood attack the foreign red blood cells by binding to them. The B antibodies in the A+ blood bind the antigens in the B+ blood and agglutination occurs. This is dangerous because the agglutinated red blood cells break after a while and their contents leak out and become toxic.
Rh factor blood grouping system:
Many people also have a so called Rh factor on the red blood cell's surface. This is also an antigen and those who have it are called Rh+. Those who haven't are called Rh-. A person with Rh- blood does not have Rh antibodies naturally in the blood plasma (as one can have A or B antibodies, for instance). But a person with Rh- blood can develop Rh antibodies in the blood plasma if he or she receives blood from a person with Rh+ blood, whose Rh antigens can trigger the production of Rh antibodies. A person with Rh+ blood can receive blood from a person with Rh- blood without any problems.