Rh is short for Rhesus factor. You're right, it's that +/- thing. There are 5 different genetic types for Rh+ and only one Rh-, hence the latter is rather rare. Many Europeans and some Northern Africans have it, but among Asians and most Africans it is quite uncommon. Only Rh- mothers with a Rh+ partner (and therefore Rh+ offspring) have this pregnancy problem.
Usually, the blood transfer between mother and baby works only one way: her blood gets into the fetus via the umbellical cord, whereas no blood of the baby gets into her system until a few days before birth.
Unfortunately, a Rh- mother will develop antibodies against a Rh+ child's blood. With the first one, it's usually no prob because the mother's immune reaction to the baby's blood starts too late to do much damage.
However, with the second and any further Rh+ pregnancies, the mother will have a full-size immuno attack standing by. And this time it doesn't wait for the baby's blood to get into contact with hers. As soon as her blood (which by then already contains antibodies) enters the fetus, it starts to attack the fetus' own blood cells. This does critical damage to the fetus and unless treated in time, the baby will be stillborn, usually at a very early stage.