Another term for basically the same kind of speech is "motherese", but most developmental psychologists in the field avoid this word. They point out that everyone, not just mothers, speak in special ways to young children. The features of child directed speech vary with the age of the child.
For instance, speech to babies who are too young to understand individual words tends to be rather high pitched and musical. Mothers in particular, but fathers as well, raise the fundamental frequency of their voices when talking to babies, and they vary their pitch much more than they do when talking to adults.