In the waning stages of pregnancy there is an increase in mom's estrogen levels.   One of the purposes of the estrogen to help make her ligaments a little more "loose" in order to facilitate labor.

That estrogen crosses the placenta and has several effects in the babies.  The kids, both boys and girls, will get hard lumps right underneath the nipple.  They can be larger than pea size, can happen only on one side, and sometimes will secrete milk (they used to call it "witch's milk").  You don't want to express the milk intentionally, because that will make more milk and can lead to infection.

An infected breast is red, hot and tender.  the baby may have a fever and be acting cranky.  If you are worried about that possibility, then I should see you and your child.

Older infant girls may sometimes have breast development that sticks around (it's called premature thelarche.) It runs in female members of families and probably indicates an increased sensitivity of the little girl's estrogen receptors. As long as there are no other signs of advancing puberty, like pubic or armpit hair, then the condition is totally benign and we don't need to do any other evaluation.  The breast development usually does not progress until it's supposed to in puberty.