What is the thin hair covering the surface of my baby's body?

Lanugo. The hair is called lanugo, it will disappear after a short time.
Lanugo. Lanugo is a thin, fine downy hair that is the first hair produces by the developing fetus' hair follicles. It starts at 3 months gestation and continues through the 9th month. At birth some babies are born with that fine hair that eventually falls off.
Lanugo. The thin, fine hair covering the surface of the baby's body is most likely lanugo. Lanugo is more common in premature babies, and becomes less prominent as the baby progresses towards his due date.
Some babies may have a more permanent distribution in keeping ethnicity. This is notassociated with any health problem and does not geberally prove to be cosmetically unacceptable.
Lanugo. At birth very often babies bodies are covered in areas with soft hair called lanugo. This hair will disappear over the next weeks.
Vellus hair. Fine colorless vellus hair (sometimes called peach fuzz) is normal on babies. Lanugo hair (another type of fine hairs) forms earlier and can be seen on premature babies. Lanugo hair is replaced by vellus hair as a baby matures.
Lanugo hair. I presume your baby is a newborn, this hair type is not coarse and is transient, will most likely regress within 6 months. No treatment is necessary for this condition.
Some babies may have darker coarser hair localized along the spine usually the lower back, this kind of hair distribution will need to be evaluated by a health care provider to screen for abnormalities of the spine.