The four basic blood groups or types, in order of frequency from most common to rarest, are O, A, B, and AB. Blood type is determined by "alleles," or possible types of a gene, that we inherit from our parents.
The different blood types reflect the possible combinations of protein molecules called antigens, which are found on the surface of the red blood cells, and antibodies, which are in the plasma.
Just as when a disease invades the body, antibodies in the blood will attack certain antigens. This means that not all human blood is compatible.
If someone were to be given a transfusion with blood that contains antibodies that are hostile to antigens in his own blood, for example, he might die from a reaction that causes red blood cells to "clump," clogging blood vessels, or to "crack," leaking hemoglobin into the body with toxic effects.
O-negative blood lacks antigens, so people with O-negative blood have been considered "universal donors," whose blood would work harmlessly in anyone's body. It turns out that even some O-negative blood can react with some rare blood types, so the concept of the "universal donor" is now a conditional one, even though O-negative blood will still be given in an emergency if a patient's blood type is not known.
Conversely, people with AB-positive blood in general can receive any type of blood because that type does not contain antibodies that attack the A or the B antigens. (Type O blood lacks those antigens.)
The "plus" and "minus" in blood types refers to a particular antigen called "the Rh factor." Anyone can receive blood without the Rh factor, but only people with the Rh factor can safely receive blood that contains it.
If a pregnant woman needs a blood transfusion during or after labor — rare but possible — she will receive only blood that is compatible with her own — ideally her own specific blood type.