Paediatric is an adjective. It means “about the medical care of children”. A paediatric ward is the children’s part of a hospital; paediatric nurses look after babies and young people, not adults. Though actually, the given schoolbook line (“the area of medicine…”) is the noun paediatrics. People do say “I work in paediatric medicine,” but paediatric by itself is the describing word, like dental in dental clinic. It is a normal hospital word, not slang. British spelling keeps ae; American English writes pediatric.