In Tolkien's fiction, The Children of Ilúvatar refers to Elves and Men. Dwarves are not included in this, as though they were given sapience by Ilúvatar, they were in fact created by Aulë.

Elves are also named the Quendi ("those who speak", in Quenya) and the Minnónar¹ ("Firstborn"). They are further divided into many groupings.

Men are also named the Apanónar ("Those born after" or "Afterborn"), Fírimar ("Mortals"), Engwar ("the Sickly"), and the Followers. These somewhat derogatory names were of course given to them by the Elves, who were the primary historians.

The reason for this naming is simple. Elves were the first of the Children of Ilúvatar to appear in Middle-earth, whereas Men were not to follow until the beginning of the First Age, with the creation of the Sun and Moon, many thousands of years later.

References

1. Ardalambion, "English-Quenya Wordlist" cites The War of the Jewels p. 403.