I'm sure you've heard of the A,B,O blood groups, where a person is either group A, B, AB or O. Well, the positive or negaitive refers to the Rhesus factor, which another type of blood group.
A person is grouped according to their A, B, AB or O status and then they are also grouped according to whether they have the Rhesus antibody or not. If they do, they are positive, if not they are negative.
So, if somebody is A+ they have blood group A and they also have the Rhesus antibody. If they are A- then they are blood group A but they do not have the Rhesus antibody.
There are other blood antibodies apart from the ABO system and the Rhesus system but they are rarer and not often mentioned. They do exist however. That is why if somebody needs a blood transfusion they are fully cross-matched to ensure total compatibility.