Rh incompatibility is a condition in which a pregnant person with Rh-negative blood carries a baby with Rh-positive blood. Her immune system may make antibodies that attack the baby's red blood cells.
The Rh factor is a protein that can be found on the surface of red blood cells. People who have it are Rh-positive, and people who do not are Rh-negative. Being Rh-negative is not a health problem in itself. It only matters in pregnancy if the baby has inherited Rh-positive blood from the other parent.
Rh incompatibility becomes a problem when the baby's blood enters the mother's bloodstream. This can happen at birth, during bleeding in pregnancy, after a miscarriage or ectopic pregnancy, or after some procedures. The mother's body may then make antibodies. A first pregnancy is usually not affected, but in a later pregnancy these antibodies can cross the placenta and break down the baby's red blood cells. This is called hemolytic disease of the fetus and newborn, and it can cause anemia and jaundice in newborns.
A blood test early in pregnancy shows the blood type and Rh status. Rh-negative people are usually offered injections of anti-D immunoglobulin (Rh immune globulin) during pregnancy and after certain events, which lowers the chance of the body making antibodies. If antibodies are already present, the pregnancy is monitored more closely by a specialist team.
Sources: ACOG, MedlinePlus, NHS.