This is possibly probably definitely inspired by a certain television show I've been watching recently. Summary: Dear Show, Please do not be making up your own blood groups. You are doing it wrong. Frustratedly, Me.
[For those of you who have more background in this than I do, I'm going to be skipping over a lot of the details and picky bits (such as MN grouping and other typing systems) and just covering the ABO and Rh +/- basics.]
ABO Blood Groups
Human blood type is a function of proteins on the surface of the red blood cells (RBC). Which proteins you have on your RBCs is determined by which genes for blood type you inherited from your parents (one from Mom and one from Dad). Humans have three possible versions of the gene for blood type -- A, B, and O. O is the easy one -- it indicates an absence of marker proteins, and is recessive to (masked by) both A and B. Both the A and B genes will each cause a different, distinct marker protein to be present on the surface of the RBCs. Since a person inherits two genes for blood type, it is the combination of these genes that determines what blood type you actually have (we call this your phenotype).
So how does this work? Good question. If you inherit A from both parents, you will be AA genetically, but we just call this type A. Likewise with BB producing blood type B. Now, if you inherit A from one parent and O from the other, your genetic blood type (genotype) is AO, but since O has no marker proteins, it's essentially invisible, and your blood type down at the lab (phenotype) is just A. In a similar manner BO is just type B, and OO (no marker proteins at all) is just type O. What about AB? A and B are co-dominant, which means that they will both be detectable (express) when present. If a person has both the A and B genes, then their RBCs will have both the A and B surface proteins. This is blood type AB.
Look, a chart!
A
BOAAA= AAB= ABAO= ABAB= ABBB= BBO= BOAO= ABO= BOO= O
.
Okay, But What About That +/- That Goes After the Letter?
The Rh factor is another marker on the surface of RBCs that people either have (Rh+, dominant) or don't (Rh-, recessive). Like blood type, it's inherited from your parents. An inherited combination of either Rh+/Rh+ or Rh+/Rh- genes will result in an individual having Rh+ blood, and only Rh-/Rh- will result in an Rh- blood type.
Please note that there are many many different Rh antigens, and the common +/- is used only to designate the presence or absence of the most common antigen (D).
But What Does This Mean?
Those little surface proteins (antigens) on cells are (along with other stuff) one of the ways your body's immune system recognizes what's you (self) and what's an invader that needs to be destroyed (not-self). The practical upshot of this is that if you (or your character in a fic) have blood type A, your immune system is going to recognize those protein markers for A as being okay. If you were to transfuse blood with different markers (B), then the immune system will attack the foreign blood and you (or your character) will probably get very very sick or die in a
transfusion reaction.
So, can people only accept their own blood type? Well, no. If you've ever watched a medical drama you've heard surgeons calling out for units of O-neg, stat, because O- lacks those antigens that cause reactions, and is considered to be the universal donor. Likewise a person with AB+ will recognize all the markers we've talked about, and is called the universal recipient. But generally, it's best to have your own blood, or your own type that is carefully matched in a lab by people who really know what they're doing.
"Rare" Blood Types
The frequency of blood types and Rh will vary geographically and by ethnicity. In very broad terms, O+ and A+ are the most common globally (although B+ is more common than A+ in Asia), with AB- being the least common. There are many more factors than ABO groups that contribute to the designation of a rare blood type, but those are beyond the scope of this post.
For more information:
Blood, the Journal of the American Society of HematologyRed Cross Blood TypesUniversity of Arizona Blood Types Tutorial (has a couple of neat calculators)Wikipedia Blood Type (good information about population frequencies here)Wikipedia Rh Blood GroupsPalomar Community College has some history and good info