The A and B refer to specific antigens, which are things that can create antibody reactions. “O” just means that neither the A nor the B antigens are present.
These antigens are on the outside of the red blood cells. Give A, B, or O blood to someone with an AB blood type and their blood doesn’t react - they “detect” it as normal because it matches their own blood cells.
An O person who gets A, B, or AB blood has their immune system react to a “foreign” invader and the body goes berserk.
A and B are (simplistically) types of antigens, or things against which you might have an antibody. If you have an antibody against either A or B, and you get blood with that antigen, your blood will attack the red blood cells being transfused, which would be Bad.
So, type O people have anti-A and anti-B antibodies, so if they get either A, B or AB blood, it will be attacked.
Type AB people have no antibodies, so they can accept anything,
Type O people have no antigens, so nothing will attack it (there is no “anti-O antibody”)
“A” and “B” are the names of proteins on the red blood cells that can cause immune system reactions. Type O blood doesn’t have either A or B protein, which means it can be given to anyone without causing an immune system reaction. Type AB blood, on the other hand, has both proteins on it, which means that if it’s given to anyone whose immune system reacts to either the A or the B protein, it’ll cause an immune system reaction. Does that make sense?
In other words, if you were to give AB blood to somebody with the A blood type, their body would react to the B protein, and they’d get sick. If you gave it to somebody with the B blood type, their body would react to the A protein, and they’d get sick. If you gave it to somebody with the O blood type, their body would react to both the A protein and the B protein.
Frankly, it’s not that cut and dried. A person with O-type blood may have a single protein synthesis defect that prevents him from making the B antigen. If that person marries someone with AB blood, their offspring may inherit not only the A from the AB parent, but could also inherit the corrected gene for making the B antigen. Voila, AB offspring from AB and O parents.
Rh + and - are separate. If you’re Rh+, you don’t make antibodies against the Rh factor, so you can accept Rh+ or - blood. If you’re Rh-, you’ll see the Rh factor as foreign and attack it, so you can only accept Rh- blood.
Slight nitpick, you only make antibodies against Rh+ after the first exposure. So that means someone who is Rh- can get Rh+ once. If they receive it a second time they will have a immune response, but not the first time.