This passage is basically the first part of the creation myth that Tolkien designed for the world he wrote about. It tells about how Ilúvatar sang the Ainur into being and how the world and elements became real. The story mainly deals with Ilúvatar's vision and design of the world - through music.
The first part of the chapter "The Music of the Ainur" consists of a text which picks up from where the "Cottage of Lost Play" ended. It mainly describes a meeting between Eriol and aged Rúmil who dwells at the cottage and cares for the garden. This part forms a link between the "Cottage of Lost Play" and the tale of "The Music of the Ainur".