Pediatrics (also spelled paediatrics) is the branch of medicine that deals with the medical care of infants, children, and adolescents (from newborn to age 14-21, depending on the country). The word pediatrics is derived from two Greek words pais (παῖς) which means "child" and iatros (ἰατρός) which means "doctor". Most pediatricians are members of a national body, such as the American Academy of Pediatrics, the Canadian Paediatric Society, the Royal College Of Paediatrics and Child Health, Norsk barnelegeforening (The Norwegian society of pediatricians) or the Indian Academy of Pediatrics.
Pediatrics differs from adult medicine in many respects. The obvious body size differences are paralleled by maturational changes. The smaller body of an infant or neonate is substantially different physiologically from that of an adult. Congenital defects, genetic variance, immunology, oncology, and a host of other issues are unique to the realm of pediatrics.
Some diseases, such as sickle cell anemia and cystic fibrosis are more often treated by pediatricians because only recently did the majority of these patients survive into adulthood. Issues revolving around infectious diseases and immunizations are also dealt with primarily by pediatricians. Put simply, treating a child is not like treating a miniature adult.
Further training in all sub-specialties is available for pediatricians. Pediatric cardiologists deal with heart conditions in children, particularly congenital heart defects, pediatric oncologists often treat leukemias and lymphomas. Every subspecialty of the adult doctor exists in the pediatric field (with the exception of geriatrics), but some are unique to pediatrics, such as adolescent medicine, and neonatology. Specialty medicine can be very similar to those in adults, though often the diseases seen in children are not seen in adults (such as bronchiolitis) and those seen in adults are rare in children (coronary artery disease).
Childhood is the period of greatest growth, development and maturation of the various organ systems in the body. Years of training and experience (above and beyond basic medical training) goes into recognizing the difference between normal variants and what is actually pathological.
Another major difference between pediatrics and adult medicine is that children are minors and, in most jurisdictions, cannot make decisions for themselves. The issues of guardianship, privacy, legal responsibility and informed consent must always be considered in every pediatric procedure. In a sense, pediatricians often have to treat the parents and sometimes, the family, rather than just the child. Adolescents are in their own legal class, having rights to their own health care decisions in certain circumstances only, though this is in legal flux and varies by region.
In the U.S., pediatricians are considered to be primary care doctors, along with family practice, internal medicine, and obstetrics. Much of the rest of the world considers them specialists, and parents are only referred to pediatricians for special care not handled by the generalists.
Abraham Jacobi is considered the father of pediatrics.

Further reading

Contemporary Pediatrics - a monthly magazine