Eru Iluvatar, or The One
Eru (Quenya Tengwar: `V7U; IPA: [ˈeru]; the One), also called Ilúvatar (full spelling `Bj~MyE1E6 or vowel-abbreviated spelling `BjUMy16; [iˈluːvatar]; the All High or the Father of All as defined in the index of name elements in The Silmarillion), was the supreme deity of Arda and Middle-earth. He is the single creator, but has delegated most direct action within Eä to the Ainur, including the shaping of the Earth (Arda) itself. Eru is an important part of the stories of The Silmarillion but is not mentioned by name in Tolkien's most famous works, The Hobbit and The Lord of the Rings (he is alluded to as "the One" in the part of LotR's Appendix A that speaks of the downfall of Númenor).
Eru as Creator God
Elves and Men were created by Eru directly, without delegation to the Ainur, and they are therefore called "Children of Ilúvatar" (Eruhini). The Dwarves were created by Aulë with the belated approval of Ilúvatar, though they would be second to the Children of Ilúvatar.
The first things that Iluvatar created were the Ainur (from his thoughts). He then bade the Ainur to sing to him; this was called the Ainulindalë, or the music of the Ainur. Melkor created a discord to the music, and Iluvatar added three themes to the Ainulindale, which talked about the fate of Arda.
The next thing he made was Ea, the World and All That Is, and Ea was in the Void (Melkor was drawn to the Void, and so at the beginning of Arda, he lay in the Void, or the Outside as it was sometimes called). He then gave the Ainur the option to go into Ea and fashion as they will. The most powerful Ainur who chose to do so were called the Valar, and they controlled the shaping of the Arda. They could not make life, however, as Aulë proves, who was able to give only shape to the dwarves, while consciousness was given to them by Eru. The Valar were accompanied by the Maiar. The elves and men, however, came directly from Iluvatar's thoughts, and are referred to in The Silmarillion as The First Children of Iluvatar and the Second Children of Iluvatar, respectively, while the dwarves would be the Adopted Children.
Intervention
One of the only times that Eru ever intervened in the world was in the downfall of Numenor when the Valar called for his aid.