Blood groups are primarily categorized by the ABO system (A, B, O) and the Rh factor, which can be either positive (+) or negative (-). Blood incompatibility, in the context of pregnancy, refers to a mismatch between the mother's and the baby's blood types. The most common and clinically significant type is Rh incompatibility, which occurs when an Rh-negative mother is carrying an Rh-positive baby.