Believe it or not, children's music is a genre composed for children. Shock horror! Though for entertainment, it also has educational aspects- and, in some cases, has been used as a form of propaganda (linked to indoctrination). Early pieces in this genre include School Days (Gus Edwards and Will Cobb, 1907) and, possibly more famously, Teddy Bears Picnic.
Disney has had a strong influence in this genre, with scores to various films becoming children's hits, paving the way for similar ventures with other soundtracks as well as groups specifically based in the genre.
I couldn't resist a bit of Jack Johnson here!
The Sharing Song- Jack Johnson
I Wanna Be Like You- The Jungle Book
The Wheels On The Bus