They're colourful, often silly, plus they use patterns of sound and rhythm which are predictable and pleasing for the ear. Many of them could be accompanied by fun actions. All of this makes them easier to remember than sentences.
Children love to hear the same songs and stories repeatedly. It gives them chance to practise their newly developing skills on pieces in which they are already familiar. When youngsters are given the chance to use material they feel comfortable with, they realize that they gain mastery over additional skills and become confident in with these.
Before children can be good talkers they need good listening skills. Children must develop the ability to remember the sounds and words they hear, and, later, to repeat them. This is whats called auditory memory. Children have to have a good auditory memory being good communicators.
Lots of children, though, need help to develop their auditory memory, particularly if they have had times of hearing loss at any stage in infancy, such as when they have had ear infections.
Nursery rhymes are excellent for practising auditory memory skills. In the fun sort of way they learn how to remember exact sequences of sounds and words. And the words can often be teamed with actions, which kids love, before they even say the words. Songs which have actions are even easier to remember. The actions profit the words come.
Nursery Rhymes allow for endless repetition which means that your child is practising words and phrases many times.