This is the test that is done on the newborn's blood sample, usually in the setting of a newborn with jaundice. The test is looking for "foreign" antibodies that are already adhered to the infant's rbcs, a potential cause of hemolysis. This is referred to as "antibody-mediated hemolysis". The two most commonly recognized forms of antibody-mediated hemolysis in newborns are Rh incompatibility and ABO incompatibility.
Rh incompatibility occurs when a mother who is type Rh - (and has naturally occuring anti-Rh antibodies in her serum) gives birth to an infant who is Rh+. If any mixing of maternal and fetal blood occurs during pregnancy or the birth process, the mother's anti-Rh antibodies will vigorously attack the baby's Rh+ rbcs by adhering to, and then lysing, the cells.
ABO incompatibility occurs by the same general mechanism. Type O mothers are most commonly impacted, since they carry both anti-A and anti-B antibodies. If the infant is type A, type B, or type AB, risk for incompatibility exists. This is frequently referred to as a "set-up". If mixing of maternal and fetal blood occurs during pregnancy or the birth process, these antibodies can also attack the baby's rbcs and cause hemolysis. In general, this reaction is less serious than Rh incompatibility (which can be fatal if severe and untreated), and usually only results in jaundice and mild anemia.
An important thing to remember is that the presence of a positive coombs' test in the lab does not necessarily result in hyperbilirubinemia in the infant. The risk of needing phototherapy is certainly greater, but there are many factors impacting bilirubin levels, and assessment of all of these elements is critical to making an appropriate decision about treatment.
Conversely, active hemolysis may be present with a negative coombs' test. Conditions that cause the rbc to be inherently defective in some way (hereditary spherocytosis, G6PD deficiency, etc) can also result in severe hyperbilirubinemia, but because these process do not involve antibodies, the coombs' test will be negative.