Children of Ilúvatar
The Children of Ilúvatar are the two races of Elves and Men. Their existence, along with the Universe in which they were to live, was conceived in the Music of the Ainur, but the Ainur had no part in their making. Ilúvatar alone brought them into being, and they had fëar (spirits) of the same type as the Ainur, though far less powerful.
Unlike the Ainur, however, the Children were intended to exist as a union of flesh and spirit; their bodies, or hröar, are as integral to their being as their fëar. As such, they are also called Mirröanwi, or Incarnates.
While their status as embodied souls created by Ilùvatar makes them extraordinarily alike, each Kindred of the Children was also bestowed with different gifts from their maker. The Elves received great beauty, near immortality, skill with arts and crafts, and keen memories. Men, on the other hand, were given freedom to act outside the boundaries set by the Music of the Ainur, eventual supremacy over Middle-earth, and mortality.
The Dwarves, while also incarnates, are not typically called Children of Ilúvatar, for though they were given sapience and independent being by Eru, they were in fact created by Aulë. When Eru gave 'blessing' to Aulë's work, he distinguished the Dwarves by Elves and Men calling them "the children of my adoption" (The Silmarillion) while calling Elves and Men "the children of my choice."