Children of Ilúvatar
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, though Ilúvatar adopted them and gave them independent being.
Men are also named Atani ("Second People"), Hildor ("the Followers" or "the Aftercomers"), Apanónar ("Those born after" or "Afterborn"), Fírimar ("Mortals"), Engwar ("the Sickly"), the Heavy-handed, the Inscrutable, the Night-fearers, the Self-cursed, the Strangers, the Usurpers, and the Children of the Sun. 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.