A universal recipient is a person with the AB blood type. They can receive a blood transfusion, or even a donated organ, from a person with any blood type. To put it another way, the immune system of a person with AB blood will accept blood from all possible donors.
So how is it that the rarest blood type is also the one that is a universal recipient? The answer lies in the antigens that are present in most blood types. O blood types have no antigens, A blood types have a specific antigen, as do B blood types. AB blood type means that the antigens for A and B blood are both present.
Since both A and B antigens are present in a person with AB blood, the recipient won't reject the blood. O blood has no antigens, and is referred to as universal donor blood, so that will not cause a reaction.
Keep in mind that there is a difference between a reaction caused by the transfusion of the wrong type of blood, which can be fatal, and an allergic reaction to the transfusion of blood, which is possible regardless of blood type.
50 Quick Facts. The American Red Cross. Accessed October, 2010. http://www.givelife2.org/sponsor/quickfacts.asp