Inverted nipples are nipples which turn inwards. Provided they have always been inverted they are not a problem. Breast feeding is possible although you and the baby may need to be patient and to put a bit more effort into it.
Most women's nipples protrude (stick out) about 5–10 mm. Usually they become about 10 mm longer and 2–3 mm wider during sexual arousal. Some women have nipples that are flat, but become erect during sexual arousal or when a baby is sucking on the nipple. Nipples that are tucked into the breast, instead of being flat or sticking out, are called inverted nipples. Both nipples may be inverted, or just one.
A truly inverted nipple is caused by adhesions at the base of the nipple that bind the skin to the underlying tissue. While the skin does become more elastic during the third trimester of pregnancy in preparation for nursing, some of the cells in the nipple and areola may stay attached. Sometimes the stress of vigorous nursing will cause the adhesion to lift up rather than stretching or breaking loose, and this can cause cracks in the nipple tissue and pain for the mother. Inverted nipples are usually a result of the ligaments along the milk ducts which run to the nipples (and the ducts themselves) as shorter than the distance from from the center of the breast where they originate to the nipple. Hence they pull in end of the nipple in toward the center of the breast, inverting it. This is the second thing to note.
Inverted nipples are one of the many variations of the human body that make each of us unique, sort of like having an "innie" or "outtie" bellybutton. Some people feel awkward about having "innies" because their nipples look different or appear to be hiding or are shy. Fortunately, no medical problems are associated with being born with inverted nipples.
It's possible to change "innie" nipples to "outties" through plastic surgery. These procedures are expensive, though (ranging from about two to five thousand dollars), and there's a chance that nipples will revert to their old orientation after the operation. Talk with your pediatrician or adolescent health care provider. S/he may have additional info or insight for you, including what is normal for men and what's involved in surgery.
Inverted nipples don't need to be a cause for concern. Actually 28 to 35 percent of women who are pregnant for the first time have nipples that don't extend well.